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parse_rhs.py
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parse_rhs.py
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#!/usr/bin/python2
import sys
#rhs="-(-r^3*cos(theta) + r^2*(2*r - 13/5)*cos(theta) + 13*r^2*cos(theta)/5 + 2*r*(-r + 13/10)^2*cos(theta) + r*(2*r^2*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*(-r + 13/10)^2*cos(theta)) - 169*r*cos(theta)/100)/r;"
#rhs="-(-r^3*cos(theta) +pow( r, 2)*(2*r - 13/5)*cos(theta) + 13*pow(r, 2)*cos(theta)/5 + 2*r*pow(-r + 13/10, 2)*cos(theta) + r*(2*pow(r, 2)*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*pow(-r + 13/10, 2)*cos(theta)) - 169*r*cos(theta)/100)/r;"
#rhs="-(-pow(r, 3)*cos(theta) +pow( r, 2)*(2*r - 13/5)*cos(theta) + 13*pow(r, 2)*cos(theta)/5 + 2*r*pow(-r + 13/10, 2)*cos(theta) + r*(2*pow(r, 2)*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*pow(-r + 13/10, 2)*cos(theta)) - 169*r*cos(theta)/100)/r;"
#rhs = "-(-12553587811485704*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))/(3242591731706757*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(2*r^2*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*(-r + 13/10)^2*cos(theta)) + (r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-r^3*cos(theta) + 13*r^2*cos(theta)/5 - 169*r*cos(theta)/100))/r;"
#rhs = "-(-12553587811485704*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))/(3242591731706757*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(2*pow(r, 2)*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*pow(-r + 13/10, 2)*cos(theta)) + (pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-pow(r, 3)*cos(theta) + 13*pow(r, 2)*cos(theta)/5 - 169*r*cos(theta)/100))/r;"
#rhs="(4/((obj.kappa + 1)^2*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)) + (32*obj.delta^2*y^2)/((obj.kappa - 1)^2*(obj.kappa + 1)^4*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2) + (4*obj.delta^2*((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2))/((obj.kappa - 1)^2*(obj.kappa + 1)^2*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2) + (32*obj.delta^4*y^2*((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2))/((obj.kappa - 1)^4*(obj.kappa + 1)^4*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^3) + (16*obj.delta^4*y^2*((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2))/((obj.kappa - 1)^4*(obj.kappa + 1)^4*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(3/2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2))/(2*(((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1))^(1/2)) + (4/((obj.kappa - 1)^2*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)) + (2*((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)*(((4*obj.delta*((2*obj.delta*x)/(obj.kappa - 1)^2 - 1))/(obj.kappa - 1)^2 - (8*obj.delta^2*x)/(obj.kappa - 1)^4)/(2*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)) - (2*obj.delta)/(obj.kappa - 1)^2)^2)/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^3 - (8*x*(((4*obj.delta*((2*obj.delta*x)/(obj.kappa - 1)^2 - 1))/(obj.kappa - 1)^2 - (8*obj.delta^2*x)/(obj.kappa - 1)^4)/(2*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)) - (2*obj.delta)/(obj.kappa - 1)^2))/((obj.kappa - 1)^2*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2) + (((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)*((4*obj.delta*((2*obj.delta*x)/(obj.kappa - 1)^2 - 1))/(obj.kappa - 1)^2 - (8*obj.delta^2*x)/(obj.kappa - 1)^4)^2)/(4*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(3/2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2))/(2*(((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1))^(1/2)) - ((4*x)/((obj.kappa - 1)^2*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)) - (((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)*(((4*obj.delta*((2*obj.delta*x)/(obj.kappa - 1)^2 - 1))/(obj.kappa - 1)^2 - (8*obj.delta^2*x)/(obj.kappa - 1)^4)/(2*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)) - (2*obj.delta)/(obj.kappa - 1)^2))/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2)^2/(4*(((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1))^(3/2)) - ((4*y)/((obj.kappa + 1)^2*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)) + (4*obj.delta^2*y*((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2))/((obj.kappa - 1)^2*(obj.kappa + 1)^2*(((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2)*((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1)^2))^2/(4*(((2*x^2)/(obj.kappa - 1)^2 + (2*y^2)/(obj.kappa + 1)^2)/((((2*obj.delta*x)/(obj.kappa - 1)^2 - 1)^2 - (4*obj.delta^2*(x^2/(obj.kappa - 1)^2 + y^2/(obj.kappa + 1)^2))/(obj.kappa - 1)^2)^(1/2) - (2*obj.delta*x)/(obj.kappa - 1)^2 + 1))^(3/2));"
#rhs="(4/(pow(obj.kappa + 1, 2)*((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1)) + (32*pow(obj.delta, 2)*pow(y, 2))/(pow(obj.kappa - 1, 2)*(obj.kappa + 1)^4*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)) + (4*pow(obj.delta, 2)*((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2)))/(pow(obj.kappa - 1, 2)*pow(obj.kappa + 1, 2)*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)) + (32*obj.delta^4*pow(y, 2)*((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2)))/((obj.kappa - 1)^4*(obj.kappa + 1)^4*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 3)) + (16*obj.delta^4*pow(y, 2)*((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2)))/((obj.kappa - 1)^4*(obj.kappa + 1)^4*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(3/2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)))/(2*(((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))/((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1))^(1/2)) + (4/(pow(obj.kappa - 1, 2)*((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1)) + (2*((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))*pow(((4*obj.delta*((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1))/pow(obj.kappa - 1, 2) - (8*pow(obj.delta, 2)*x)/(obj.kappa - 1)^4)/(2*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)) - (2*obj.delta)/pow(obj.kappa - 1, 2), 2))/pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 3) - (8*x*(((4*obj.delta*((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1))/pow(obj.kappa - 1, 2) - (8*pow(obj.delta, 2)*x)/(obj.kappa - 1)^4)/(2*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)) - (2*obj.delta)/pow(obj.kappa - 1, 2)))/(pow(obj.kappa - 1, 2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)) + (((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))*pow((4*obj.delta*((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1))/pow(obj.kappa - 1, 2) - (8*pow(obj.delta, 2)*x)/(obj.kappa - 1)^4, 2))/(4*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(3/2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)))/(2*(((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))/((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1))^(1/2)) - pow((4*x)/(pow(obj.kappa - 1, 2)*((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1)) - (((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))*(((4*obj.delta*((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1))/pow(obj.kappa - 1, 2) - (8*pow(obj.delta, 2)*x)/(obj.kappa - 1)^4)/(2*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)) - (2*obj.delta)/pow(obj.kappa - 1, 2)))/pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2), 2)/(4*(((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))/((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1))^(3/2)) - pow((4*y)/(pow(obj.kappa + 1, 2)*((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1)) + (4*pow(obj.delta, 2)*y*((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2)))/(pow(obj.kappa - 1, 2)*pow(obj.kappa + 1, 2)*(pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2)*pow((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1, 2)), 2)/(4*(((2*pow(x, 2))/pow(obj.kappa - 1, 2) + (2*pow(y, 2))/pow(obj.kappa + 1, 2))/((pow((2*obj.delta*x)/pow(obj.kappa - 1, 2) - 1, 2) - (4*pow(obj.delta, 2)*(pow(x, 2)/pow(obj.kappa - 1, 2) +pow( y, 2)/pow(obj.kappa + 1, 2)))/pow(obj.kappa - 1, 2))^(1/2) - (2*obj.delta*x)/pow(obj.kappa - 1, 2) + 1))^(3/2));"
#rhs="-(4*delta_e*r^2*(-r + 13/10)^2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r^2*(-r + 13/10)^2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) - 2*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 2*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*kappa_eps*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 2*r^2*(-r + 13/10)^2*(-delta_e*kappa_eps + delta_e)*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 2*r^2*(2*r - 13/5)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*r*(-r + 13/10)^2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + r*(2*r^2*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + ((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-r^3*cos(theta) + 13*r^2*cos(theta)/5 - 169*r*cos(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-r^2*(2*r - 13/5)*sin(theta) - 2*r*(-r + 13/10)^2*sin(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (2*(kappa_eps + 1)^2*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(4*delta_e*pow(r, 2)*pow(-r + 13/10, 2)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*pow(r, 2)*pow(-r + 13/10, 2)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) - 2*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 2*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*kappa_eps*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 2*pow(r, 2)*pow(-r + 13/10, 2)*(-delta_e*kappa_eps + delta_e)*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 2*pow(r, 2)*(2*r - 13/5)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*r*pow(-r + 13/10, 2)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + r*(2*pow(r, 2)*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-pow(r, 3)*cos(theta) + 13*pow(r, 2)*cos(theta)/5 - 169*r*cos(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-pow(r, 2)*(2*r - 13/5)*sin(theta) - 2*r*pow(-r + 13/10, 2)*sin(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (2*pow(kappa_eps + 1, 2)*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(4*delta_e*r^2*(-r + 13/10)^2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r^2*(-r + 13/10)^2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) - 2*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 2*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*delta_e*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*kappa_eps*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 2*r^2*(-r + 13/10)^2*(-delta_e*kappa_eps + delta_e)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 25107175622971408*r^2*(-r + 13/10)^2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 2*r^2*(2*r - 13/5)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*r*(-r + 13/10)^2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 12553587811485704*r*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(2*r^2*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*(-r + 13/10)^2*cos(theta))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + ((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-r^3*cos(theta) + 13*r^2*cos(theta)/5 - 169*r*cos(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-r^2*(2*r - 13/5)*sin(theta) - 2*r*(-r + 13/10)^2*sin(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (r^2*(2*r - 13/5)*cos(theta) + 2*r*(-r + 13/10)^2*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (2*(kappa_eps + 1)^2*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-r^3*sin(theta) + 13*r^2*sin(theta)/5 - 169*r*sin(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(4*delta_e*pow(r, 2)*pow(-r + 13/10, 2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*pow(r, 2)*pow(-r + 13/10, 2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) - 2*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 2*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*delta_e*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*kappa_eps*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 2*pow(r, 2)*pow(-r + 13/10, 2)*(-delta_e*kappa_eps + delta_e)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 25107175622971408*pow(r, 2)*pow(-r + 13/10, 2)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 2*pow(r, 2)*(2*r - 13/5)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*r*pow(-r + 13/10, 2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 12553587811485704*r*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(2*pow(r, 2)*cos(theta) + 4*r*(2*r - 13/5)*cos(theta) + 2*pow(-r + 13/10, 2)*cos(theta))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-pow(r, 3)*cos(theta) + 13*pow(r, 2)*cos(theta)/5 - 169*r*cos(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-pow(r, 2)*(2*r - 13/5)*sin(theta) - 2*r*pow(-r + 13/10, 2)*sin(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(r, 2)*(2*r - 13/5)*cos(theta) + 2*r*pow(-r + 13/10, 2)*cos(theta))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (2*pow(kappa_eps + 1, 2)*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-pow(r, 3)*sin(theta) + 13*pow(r, 2)*sin(theta)/5 - 169*r*sin(theta)/100)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="(4/((kappa_eps + 1)^2*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)) + (32*delta_e^2*y^2)/((kappa_eps - 1)^2*(kappa_eps + 1)^4*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2) + (4*delta_e^2*((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2))/((kappa_eps - 1)^2*(kappa_eps + 1)^2*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2) + (32*delta_e^4*y^2*((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2))/((kappa_eps - 1)^4*(kappa_eps + 1)^4*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^3) + (16*delta_e^4*y^2*((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2))/((kappa_eps - 1)^4*(kappa_eps + 1)^4*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(3/2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2))/(2*(((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1))^(1/2)) + (4/((kappa_eps - 1)^2*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)) + (2*((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)*(((4*delta_e*((2*delta_e*x)/(kappa_eps - 1)^2 - 1))/(kappa_eps - 1)^2 - (8*delta_e^2*x)/(kappa_eps - 1)^4)/(2*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)) - (2*delta_e)/(kappa_eps - 1)^2)^2)/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^3 - (8*x*(((4*delta_e*((2*delta_e*x)/(kappa_eps - 1)^2 - 1))/(kappa_eps - 1)^2 - (8*delta_e^2*x)/(kappa_eps - 1)^4)/(2*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)) - (2*delta_e)/(kappa_eps - 1)^2))/((kappa_eps - 1)^2*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2) + (((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)*((4*delta_e*((2*delta_e*x)/(kappa_eps - 1)^2 - 1))/(kappa_eps - 1)^2 - (8*delta_e^2*x)/(kappa_eps - 1)^4)^2)/(4*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(3/2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2))/(2*(((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1))^(1/2)) - ((4*x)/((kappa_eps - 1)^2*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)) - (((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)*(((4*delta_e*((2*delta_e*x)/(kappa_eps - 1)^2 - 1))/(kappa_eps - 1)^2 - (8*delta_e^2*x)/(kappa_eps - 1)^4)/(2*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)) - (2*delta_e)/(kappa_eps - 1)^2))/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2)^2/(4*(((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1))^(3/2)) - ((4*y)/((kappa_eps + 1)^2*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)) + (4*delta_e^2*y*((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2))/((kappa_eps - 1)^2*(kappa_eps + 1)^2*(((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2)*((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1)^2))^2/(4*(((2*x^2)/(kappa_eps - 1)^2 + (2*y^2)/(kappa_eps + 1)^2)/((((2*delta_e*x)/(kappa_eps - 1)^2 - 1)^2 - (4*delta_e^2*(x^2/(kappa_eps - 1)^2 + y^2/(kappa_eps + 1)^2))/(kappa_eps - 1)^2)^(1/2) - (2*delta_e*x)/(kappa_eps - 1)^2 + 1))^(3/2));"
#rhs="(4/(pow(kappa_eps + 1, 2)*(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1)) + (32*pow(delta_e, 2)*pow(y, 2))/(pow(kappa_eps - 1, 2)*pow(kappa_eps + 1, 4)*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)) + (4*pow(delta_e, 2)*((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2)))/(pow(kappa_eps - 1, 2)*pow(kappa_eps + 1, 2)*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)) + (32*pow(delta_e, 4)*pow(y, 2)*((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2)))/(pow(kappa_eps - 1, 4)*pow(kappa_eps + 1, 4)*(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 3)) + (16*pow(delta_e, 4)*pow(y, 2)*((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2)))/(pow(kappa_eps - 1, 4)*pow(kappa_eps + 1, 4)*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (3/2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)))/(2*pow(((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))/(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1), (1/2))) + (4/(pow(kappa_eps - 1, 2)*(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1)) + (2*((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))*pow(((4*delta_e*((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1))/pow(kappa_eps - 1, 2) - (8*pow(delta_e, 2)*x)/pow(kappa_eps - 1, 4))/(2*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))) - (2*delta_e)/pow(kappa_eps - 1, 2), 2))/pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 3) - (8*x*(((4*delta_e*((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1))/pow(kappa_eps - 1, 2) - (8*pow(delta_e, 2)*x)/pow(kappa_eps - 1, 4))/(2*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))) - (2*delta_e)/pow(kappa_eps - 1, 2)))/(pow(kappa_eps - 1, 2)*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)) + (((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))*pow((4*delta_e*((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1))/pow(kappa_eps - 1, 2) - (8*pow(delta_e, 2)*x)/pow(kappa_eps - 1, 4), 2))/(4*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (3/2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)))/(2*pow(((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))/(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1), (1/2))) - pow((4*x)/(pow(kappa_eps - 1, 2)*(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1)) - (((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))*(((4*delta_e*((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1))/pow(kappa_eps - 1, 2) - (8*pow(delta_e, 2)*x)/pow(kappa_eps - 1, 4))/(2*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))) - (2*delta_e)/pow(kappa_eps - 1, 2)))/pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2), 2)/(4*pow(((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))/(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1), (3/2))) - pow((4*y)/(pow(kappa_eps + 1, 2)*(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1)) + (4*pow(delta_e, 2)*y*((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2)))/(pow(kappa_eps - 1, 2)*pow(kappa_eps + 1, 2)*pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2))*pow(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1, 2)), 2)/(4*pow(((2*pow(x, 2))/pow(kappa_eps - 1, 2) + (2*pow(y, 2))/pow(kappa_eps + 1, 2))/(pow(pow((2*delta_e*x)/pow(kappa_eps - 1, 2) - 1, 2) - (4*pow(delta_e, 2)*(pow(x, 2)/pow(kappa_eps - 1, 2) +pow( y, 2)/pow(kappa_eps + 1, 2)))/pow(kappa_eps - 1, 2), (1/2)) - (2*delta_e*x)/pow(kappa_eps - 1, 2) + 1), (3/2)));"
#rhs="-(4*pi^2*r^3*sin(theta)^2*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 8*pi^2*r^3*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta)) + 4*pi^2*r^3*sin(2*pi*r*sin(theta))*cos(theta)^2*cos(2*pi*r*cos(theta)) + 2*pi*r^2*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 2*pi*r^2*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) + r*(-8*pi*r*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) + 8*pi*r*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) - 4*pi^2*(-r^2 + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(theta)^2*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 8*pi^2*(-r^2 + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta)) - 4*pi^2*(-r^2 + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(2*pi*r*sin(theta))*cos(theta)^2*cos(2*pi*r*cos(theta)) - 2*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))) - 34277272230171325358342660906025*pi^2*r*sin(theta)^2*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))/5070602400912917605986812821504 + 34277272230171325358342660906025*pi^2*r*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta))/2535301200456458802993406410752 - 34277272230171325358342660906025*pi^2*r*sin(2*pi*r*sin(theta))*cos(theta)^2*cos(2*pi*r*cos(theta))/5070602400912917605986812821504 - 2*r*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) + 2*pi*(-r^2 + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 2*pi*(-r^2 + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) - 34277272230171325358342660906025*pi*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))/10141204801825835211973625643008 + 34277272230171325358342660906025*pi*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta)/10141204801825835211973625643008)/r;"
#rhs="-(4*pow(pi, 2)*pow(r, 3)*pow(sin(theta), 2)*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 8*pow(pi, 2)*pow(r, 3)*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta)) + 4*pow(pi, 2)*pow(r, 3)*sin(2*pi*r*sin(theta))*pow(cos(theta), 2)*cos(2*pi*r*cos(theta)) + 2*pi*pow(r, 2)*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 2*pi*pow(r, 2)*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) + r*(-8*pi*r*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) + 8*pi*r*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) - 4*pow(pi, 2)*(-pow(r, 2) + 34277272230171325358342660906025/20282409603651670423947251286016)*pow(sin(theta), 2)*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 8*pow(pi, 2)*(-pow(r, 2) + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta)) - 4*pow(pi, 2)*(-pow(r, 2) + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(2*pi*r*sin(theta))*pow(cos(theta), 2)*cos(2*pi*r*cos(theta)) - 2*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))) - 34277272230171325358342660906025*pow(pi, 2)*r*pow(sin(theta), 2)*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))/5070602400912917605986812821504 + 34277272230171325358342660906025*pow(pi, 2)*r*sin(theta)*sin(2*pi*r*cos(theta))*cos(theta)*cos(2*pi*r*sin(theta))/2535301200456458802993406410752 - 34277272230171325358342660906025*pow(pi, 2)*r*sin(2*pi*r*sin(theta))*pow(cos(theta), 2)*cos(2*pi*r*cos(theta))/5070602400912917605986812821504 - 2*r*sin(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) + 2*pi*(-pow(r, 2) + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta)) - 2*pi*(-pow(r, 2) + 34277272230171325358342660906025/20282409603651670423947251286016)*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta) - 34277272230171325358342660906025*pi*sin(theta)*cos(2*pi*r*sin(theta))*cos(2*pi*r*cos(theta))/10141204801825835211973625643008 + 34277272230171325358342660906025*pi*sin(2*pi*r*sin(theta))*sin(2*pi*r*cos(theta))*cos(theta)/10141204801825835211973625643008)/r;"
#rhs="-(-2*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 2*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) - 4*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 8*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*kappa_eps*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*(4*PI*delta_e*(-r^2 + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 12553587811485704*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + ((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (2*(kappa_eps + 1)^2*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 25107175622971408*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(-2*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 2*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) - 4*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 8*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*kappa_eps*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*(4*PI*delta_e*(-pow(r, 2) + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(2*kappa_eps*sin(theta) + 2*sin(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*pow(PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 12553587811485704*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (2*pow(kappa_eps + 1, 2)*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 25107175622971408*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(2*r*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(-8*PI*r*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 8*PI*r*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta) - 4*PI^2*(-r^2 + 169/100)*sin(theta)^2*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 8*PI^2*(-r^2 + 169/100)*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta)) - 4*PI^2*(-r^2 + 169/100)*sin(2*PI*r*sin(theta))*cos(theta)^2*cos(2*PI*r*cos(theta)) - 2*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)))/(2.6 + PI) - 22.2222222222222*r*(-2*r*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 2*PI*(-r^2 + 169/100)*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*(-r^2 + 169/100)*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta))/((2.6 + PI)*((11.1111111111111*r - 11.1111111111111)^2 + 1)) + 2*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(-2*r*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 2*PI*(-r^2 + 169/100)*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*(-r^2 + 169/100)*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta))/(2.6 + PI) + 2*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(4*PI^2*r^3*sin(theta)^2*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 8*PI^2*r^3*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta)) + 4*PI^2*r^3*sin(2*PI*r*sin(theta))*cos(theta)^2*cos(2*PI*r*cos(theta)) + 2*PI*r^2*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*r^2*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta) - 169*PI^2*r*sin(theta)^2*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta))/25 + 338*PI^2*r*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta))/25 - 169*PI^2*r*sin(2*PI*r*sin(theta))*cos(theta)^2*cos(2*PI*r*cos(theta))/25 - 169*PI*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta))/50 + 169*PI*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta)/50)/(2.6 + PI))/r;"
#rhs="-(2*r*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(-8*PI*r*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 8*PI*r*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta) - 4*pow(PI, 2)*(-pow(r, 2) + 169/100)*pow(sin(theta), 2)*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 8*pow(PI, 2)*(-pow(r, 2) + 169/100)*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta)) - 4*pow(PI, 2)*(-pow(r, 2) + 169/100)*sin(2*PI*r*sin(theta))*pow(cos(theta), 2)*cos(2*PI*r*cos(theta)) - 2*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)))/(2.6 + PI) - 22.2222222222222*r*(-2*r*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 2*PI*(-pow(r, 2) + 169/100)*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*(-pow(r, 2) + 169/100)*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta))/((2.6 + PI)*(pow(11.1111111111111*r - 11.1111111111111, 2) + 1)) + 2*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(-2*r*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) + 2*PI*(-pow(r, 2) + 169/100)*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*(-pow(r, 2) + 169/100)*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta))/(2.6 + PI) + 2*(-atan(11.1111111111111*r - 11.1111111111111) + 1.3)*(4*pow(PI, 2)*pow(r, 3)*pow(sin(theta), 2)*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 8*pow(PI, 2)*pow(r, 3)*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta)) + 4*pow(PI, 2)*pow(r, 3)*sin(2*PI*r*sin(theta))*pow(cos(theta), 2)*cos(2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta) - 169*pow(PI, 2)*r*pow(sin(theta), 2)*sin(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta))/25 + 338*pow(PI, 2)*r*sin(theta)*sin(2*PI*r*cos(theta))*cos(theta)*cos(2*PI*r*sin(theta))/25 - 169*pow(PI, 2)*r*sin(2*PI*r*sin(theta))*pow(cos(theta), 2)*cos(2*PI*r*cos(theta))/25 - 169*PI*sin(theta)*cos(2*PI*r*sin(theta))*cos(2*PI*r*cos(theta))/50 + 169*PI*sin(2*PI*r*sin(theta))*sin(2*PI*r*cos(theta))*cos(theta)/50)/(2.6 + PI))/r;"
#rhs="-(-2*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*delta_e*r*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 2*delta_e*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*delta_e*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) - 4*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 8*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*kappa_eps*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + r*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*(4*PI*delta_e*(-r^2 + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + ((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (2*(kappa_eps + 1)^2*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(-2*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*delta_e*r*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*r*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 2*delta_e*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*delta_e*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) - 4*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 8*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*kappa_eps*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + r*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*(4*PI*delta_e*(-pow(r, 2) + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(2*kappa_eps*sin(theta) + 2*sin(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*pow(PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (2*pow(kappa_eps + 1, 2)*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(-2*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 4*delta_e*r*((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 8*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 2*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) - 4*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 8*delta_e*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^3) + 4*kappa_eps*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*sin(theta)^2*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*(4*PI*delta_e*(-r^2 + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))^2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 12553587811485704*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + ((kappa_eps + 1)^2*sin(theta)^2 + (2*delta_e*r + kappa_eps*cos(theta) - cos(theta))^2)*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*r^2*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*r^2*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (2*(kappa_eps + 1)^2*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*r^2*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*r^2*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*r^2 + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + 25107175622971408*(-PI*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*((36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)^2 + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) - 4*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI^2*(-r^2 + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-r^2 + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-r^2 + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*r^2 - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(kappa_eps^2 - 4*kappa_eps*sin(theta)^2 + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*(2*delta_e*r*cos(theta) + kappa_eps - 1)^2))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#rhs="-(-2*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 4*delta_e*r*(pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 8*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 2*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*delta_e*r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) - 4*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*sign(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 8*delta_e*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 3)) + 4*kappa_eps*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*pow(sin(theta), 2)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + r*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*(4*PI*delta_e*(-pow(r, 2) + 169/100)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 4*PI*r*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + 4*PI*r*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(2*kappa_eps*sin(theta) + 2*sin(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*pow(PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*pow(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta), 2)*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 12553587811485704*r*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-delta_e*kappa_eps + delta_e)*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (pow(kappa_eps + 1, 2)*pow(sin(theta), 2) + pow(2*delta_e*r + kappa_eps*cos(theta) - cos(theta), 2))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) - 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*kappa_eps*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*kappa_eps*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) + 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 + 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*kappa_eps*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*kappa_eps*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50 + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta)) + 2*PI*pow(r, 2)*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 2*PI*pow(r, 2)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta) - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*(-2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(theta)*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))/50 - 169*PI*(2*PI*kappa_eps*r*cos(theta) + 2*PI*r*cos(theta))*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(theta)*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 - 169*PI*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))*cos(theta)/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (2*pow(kappa_eps + 1, 2)*sin(theta)*cos(theta) + (-2*kappa_eps*sin(theta) + 2*sin(theta))*(2*delta_e*r + kappa_eps*cos(theta) - cos(theta)))*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*PI*kappa_eps*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*kappa_eps*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) + 169*PI*kappa_eps*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*kappa_eps*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 2*PI*pow(r, 2)*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 2*PI*pow(r, 2)*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta)) - 169*PI*sin(theta)*sin(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*sin(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50 + 169*PI*cos(theta)*cos(2*PI*kappa_eps*r*sin(theta) + 2*PI*r*sin(theta))*cos(2*PI*delta_e*pow(r, 2) + 2*PI*kappa_eps*r*cos(theta) - 2*PI*r*cos(theta))/50)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + 25107175622971408*(-PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/(3242591731706757*(kappa_eps + 1)*(pow(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757, 2) + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 2*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*cos(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) - 4*(-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-delta_e*kappa_eps*r + delta_e*r + 2*kappa_eps*cos(theta))*(2*PI*r*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - 2*PI*r*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) - 2*sin(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*cos(theta) + 2*cos(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*sin(theta) - 2*r*sin(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) -pow( PI, 2)*(-pow(r, 2) + 169/100)*(2*kappa_eps*r*cos(theta) + 2*r*cos(theta))*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta)))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta))))*sin(theta)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)) + (-1569198476435713*atan(36028797018963968*r/3242591731706757 - 36028797018963968/3242591731706757)/4503599627370496 + 20399580193664269/45035996273704960)*(-2*r*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) + PI*(-pow(r, 2) + 169/100)*(2*kappa_eps*sin(theta) + 2*sin(theta))*cos(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*cos(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))) - PI*(-pow(r, 2) + 169/100)*(-4*delta_e*r - 2*kappa_eps*cos(theta) + 2*cos(theta))*sin(PI*(2*kappa_eps*r*sin(theta) + 2*r*sin(theta)))*sin(PI*(-2*delta_e*pow(r, 2) - 2*kappa_eps*r*cos(theta) + 2*r*cos(theta))))*(pow(kappa_eps, 2) - 4*kappa_eps*pow(sin(theta), 2) + 2*kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1)/((kappa_eps + 1)*pow(2*delta_e*r*cos(theta) + kappa_eps - 1, 2)))/(r*(kappa_eps + 1)*abs(2*delta_e*r*cos(theta) + kappa_eps - 1));"
#sol="(Rmax^2-rtheta(1)^2)*cos(2*PI*x)*sin(2*PI*y);"
#sol="pow(Rmax, 2)-rthetapow(1, 2))*cos(2*PI*x)*sin(2*PI*y);"
print rhs
print ""
for nb in ["2", "3", "4", "(1/2)", "(3/2)"]:
l=len(nb)
pos=rhs.find("^"+nb)
pos_par=pos
while pos != -1:
rhs = rhs[0:pos] + ", "+nb+")" + rhs[pos+l+1:]
found=0
par=0
first=1
while not found:
pos = pos-1
if not pos:
if rhs[0]=="(":
rhs = "pow"+rhs
break
else:
print "ERROR: the first character should be '('"
break
if rhs[pos]==" ":
continue
if first:
if rhs[pos] in ["(", "+", "-", "*", "/"]:
rhs=rhs[0:pos+1]+"pow("+rhs[pos+1:]
break
if rhs[pos] == ")":
rhs = rhs[0:pos]+rhs[pos+1:]
first=0
par = par+1
continue
if rhs[pos] == "(":
par = par-1
print str(par) + " " + str(pos) + " " + rhs[pos-3:pos]
if not par and pos > 2 and (rhs[pos-3:pos]=="sin" or rhs[pos-3:pos]=="cos"):
rhs=rhs[0:pos-3]+"pow("+rhs[pos-3:pos_par-1]+")"+rhs[pos_par-1:]
break
if not par:
rhs=rhs[0:pos]+"pow"+rhs[pos:]
break
if rhs[pos] == ")":
par = par+1
continue
pos=rhs.find("^"+nb)
pos_par=pos
print(rhs)
print ""