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Topic: solving a system of nonlinear equations with a trust region dogleg
Replies: 3   Last Post: Jan 30, 2014 8:19 AM

 Messages: [ Previous | Next ]
 HAMZAH ALHARTHI Posts: 2 Registered: 1/25/14
solving a system of nonlinear equations with a trust region dogleg
Posted: Jan 25, 2014 9:32 AM

Hi, I have a system of nonlinear equations (8 equations with 8 unknowns) which I am trying to solve with the fsolve with a trust region dogleg algorithm . However, an error appears saying that :

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 2.919830e-32.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 4.423072e-33.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 3.037891e-32.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.888413e-33.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 3.161707e-32.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.279516e-33.
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 2.909762e-32.
Objective function value: 2.500083916005039E26
Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunEvals = 800 (the default value).

the function that I used is the following :

function z=hamzah2003(x)
% SOME OF THE CONSTANTS ''INPUTS' TO BE USED IN THE 8 EQUATIONS
k=4;
% experimental yield_stresses
y0=142;
y45=138;
y90=137;
yb=134;
%expermiental r-values
rexp0=0.672;
rexp45=0.606;
rexp90=0.821;
rexpb=0.820;
yref=142;
% WRITTING THE 8 EQUATIONS
z(1)=(((x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+((1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k)))^(1/2*k))-yref;
z(2)=(((x(1)*((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(x(1)*((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+((1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k)))^(1/2*k))-yref;
z(3)=(((x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+((1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k)))^(1/2*k))-yref;
z(4)=(((x(1)*(((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(x(1)*(((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+((1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k)))^(1/2*k))-yref;
z(5)=
-(((sin(0)^2)*(((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)+(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(0.5)+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*
(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)-(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))*x(3))/(sqrt((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))^2)+((x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))))+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0
))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)))*((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))*x(6))/(sqrt((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))^2)+((x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))))-((sin(0)^2)*(((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2
))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)+(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(0)+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2
*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)-(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(((x(5)^2)*(y0*cos(0)*sin(0)))/2*(sqrt((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))^2)+((x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))))+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*co
s(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)))*(((x(8)^2)*(y0*cos(0)*sin(0)))/2*(sqrt((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))^2)+((x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))))))+((cos(0)^2)*(((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))
)^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)+(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(x(2)/2)+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x
(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)-(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))*(-x(4)))/(sqrt((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))^2)+((x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))))+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)
*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)))*((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))^2)+((x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))))))/((((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)+(x(1)*((((y0*((cos(
0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(0.5)+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)-(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)
))))^(2*k-1))))*((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))*x(3))/(sqrt((0.25*(x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))^2)+((x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0))))))+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)))*((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))*x(6))/(sqrt((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^
2)))^2)+((x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))))+(((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)+(x(1)*((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1))))*(x(2)/2)+((x(1)*(((((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((c
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((y0*((cos(0))^2))+x(2))/2)+(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+x(1)*(((((y0*((cos(0))^2))+x(2))/2)-(sqrt((((x(3)*(y0*((cos(0))^2))-x(4)*(y0*((sin(0))^2)))/4)^2)+(x(5)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))/4)^2)+(x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))^(2*k-1)))*((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y0*((cos(0))^2))-x(7)*(y0*((sin(0))^2)))^2)+((x(8)^2)*(y0*cos(0)*sin(0))*(y0*cos(0)*sin(0)))))))))-rexp0;
z(6)=
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5))*(y45*cos(45)*sin(45))))))+((x(1)*(((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+x(1)*(((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1)))*(((x(8)^2)*(y45*cos(45)*sin(45)))/2*(sqrt((0.25*(x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))^2)+((x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45))))))))+((cos(45)^2)*(((x(1)*(((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y4
5*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+x(1)*(((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1)+(x(1)*((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1))))*(x(2)/2)+((x(1)*(((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*
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+((x(1)*(((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+x(1)*(((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1)))*((0.25*(x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))^2)+((x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))))))/((((x(1)*(((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(
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)*sin(45)))))^(2*k))+x(1)*(((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y45*((cos(45))^2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1)-(x(1)*((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1))))*((0.25*(x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))*(-x(4)))/(sqrt((0.25*(x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))^2)+((x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45))))))+((x(1)*(((((y45*((cos(45))^
2))+x(2))/2)+(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+x(1)*(((((y45*((cos(45))^2))+x(2))/2)-(sqrt((((x(3)*(y45*((cos(45))^2))-x(4)*(y45*((sin(45))^2)))/4)^2)+(x(5)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))/4)^2)+(x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))^(2*k-1)))*((0.25*(x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y45*((cos(45))^2))-x(7)*(y45*((sin(45))^2)))^2)+((x(8)^2)*(y45*cos(45)*sin(45))*(y45*cos(45)*sin(45)))))))))-rexp45;
z(7)=
-(((sin(90)^2)*(((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(0.5)+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x
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(90)^2)*(((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(0)+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*
((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)-(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(((x(5)^2)*(y90*cos(90)*sin(90)))/2*(sqrt((0.25*(x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))^2)+((x(5)^2)*(y90*cos(90)*sin(9
0))*(y90*cos(90)*sin(90))))))+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)))*(((x(8)^2)*(y90*cos(90)*sin(90)))/2*(sqrt((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))^2)+((x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90))))))))+((cos(90)^2)*(((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y9
0*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(x(2)/2)+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*
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+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)))*((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))^2)+((x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))))))/((((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(
90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(0.5)+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin
(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)-(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*((0.25*(x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))*x(3))/(sqrt((0.25*(x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))^2)+((x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90))))))+((x(1)*(((((y
90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)))*((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))*x(6))/(sqrt((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))^2)+((x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))))+(((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*(
(sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)+(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*(x(2)/2)+((x(1)*(((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90
)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(x(1)*((((y90*((cos(90))^2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)-(x(1)*((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1))))*((0.25*(x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))*(-x(4)))/(sqrt((0.25*(x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))^2)+((x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90))))))+((x(1)*(((((y90*((cos(90))^
2))+x(2))/2)+(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+x(1)*(((((y90*((cos(90))^2))+x(2))/2)-(sqrt((((x(3)*(y90*((cos(90))^2))-x(4)*(y90*((sin(90))^2)))/4)^2)+(x(5)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))/4)^2)+(x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))^(2*k-1)))*((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))*(-x(7)))/(sqrt((0.25*(x(6)*(y90*((cos(90))^2))-x(7)*(y90*((sin(90))^2)))^2)+((x(8)^2)*(y90*cos(90)*sin(90))*(y90*cos(90)*sin(90)))))))))-rexp90;
z(8)=
((((x(1)*((((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(x(1)*(((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1)+(x(1)*(((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1))))*(x(2)/2)+((x(1)*((((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(x(1)*(((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1)-(x(1)*(((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1))))*((0.25*(x(3)*yb-x(4)*yb)*(-x(4)))/(sqrt((0.25*(x(3)*yb-x(4)*yb)^2)+((x(5)^2)*0*0))))+((x(1)*((((yb+x(2))/2)+(
sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k-1)))*((0.25*(x(6)*yb-x(7)*yb)*(-x(7)))/(sqrt((0.25*(x(6)*yb-x(7)*yb)^2)+((x(8)^2)*0*0)))))/(((x(1)*((((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(x(1)*(((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1)+(x(1)*(((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1))))*(0.5)+((x(1)*((((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5
)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(x(1)*(((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1)-(x(1)*(((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k-1))))*((0.25*(x(3)*yb-x(4)*yb)*x(3))/(sqrt((0.25*(x(3)*yb-x(4)*yb)^2)+((x(5)^2)*0*0))))+((x(1)*((((yb+x(2))/2)+(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+x(1)*((((yb+x(2))/2)-(sqrt((((x(3)*yb-x(4)*yb)/4)^2)+(x(5)^2)*0*0)))^(2*k))+(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k))^((1/2*k)-1)*(2*(1-x(1))*(2*(sqrt((((x(6)*yb-x(7)*yb)/4)^2)+(x(8)^2)*0*0)))^(2*k-1)))*((0.25*(x(6)*yb-x(7)*yb)*x(6))/(sqrt((0.25*(x(6)*yb-x(7)*yb)^2)+((x(8)^2)*0*0))))))-rexpb;
end