MATLAB: Function numden() seems to return false solution! Where is the mistake

Question

Hey folks,

i use the numden() function to obtain numerator and denominator of two symbolic expressions. Interestingly, numden() seems to return for the first expression the correct numerator and denominator. However, for the second expression it seems that numden() does not return the correct numerator and denominator. Here is the code:

% introduce symbolic variables
syms x y z n1 n2 n3 real
% first expression
expr1 = -(n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) - n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i + n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i - n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i - n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i + n2*n3*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i + n1*n3*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i - n3^2*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) - n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) - n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) + n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) + n1*n3*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2))/abs((cos(x) + sin(x)*1i)*(n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) - n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i + n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i - n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i - n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*1i + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*1i + n2*n3*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i + n1*n3*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i - n3^2*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) - n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) - n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) + n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z) + n1*n3*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)*1i + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)));
% second expression
expr2 = ((cos(y)*1i + sin(y))*(n1^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n2^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n3^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n3^2*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n2^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n3^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) + n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*n3*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) + n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)))/(abs(sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1)*1i + (1 - (sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2)^(1/2) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2))*1i + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2))*1i)*(n1^2 + n2^2 + n3^2)^(3/2));
% compute numerator and denominator
[numExpr1, denExpr1] = numden( expr1 );
[numExpr2, denExpr2] = numden( expr2 );
% check if correct numerator and denominators were computed
check1 = simplify( expr1 - (numExpr1/denExpr1) )
check2 = simplify( expr2 - (numExpr2/denExpr2) )

The variable check1 retunrs 0 as expected. However, check2 is not zero. Instead i get the result:

check1 = 0; % return zero as expected
check2 = ((cos(y)*1i + sin(y))*(n1^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n2^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n3^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 - 1i/2) + n3^2*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n2^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n3^2*abs((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)^(1/2)*sign((sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2 - 1)*(n1^2 + n2^2 + n3^2)^(1/2)*(1/2 + 1i/2) + n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) + n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*n3*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n2*n3*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) + n1*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2)))/(abs(sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1)*1i + (1 - (sin(y)*(((cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1)*(n1^2 + n2^2))/(n1^2 + n2^2 + n3^2) + 1) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)) + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2)))^2)^(1/2) + cos(y)*cos(z)*((n2*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) - (n1*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2))*1i + cos(y)*sin(z)*((n1*sin((n1^2 + n2^2 + n3^2)^(1/2)))/(n1^2 + n2^2 + n3^2)^(1/2) + (n2*n3*(cos((n1^2 + n2^2 + n3^2)^(1/2)) - 1))/(n1^2 + n2^2 + n3^2))*1i)*(n1^2 + n2^2 + n3^2)^(3/2)) - (abs(n1^2*1i + n2^2*1i + n3^2*1i)*(cos(y)*1i + sin(y))*(2*n1^2 + 2*n2^2 + 2*n3^2)*(sign((n3^4*sin(y)^2 - n1^4 - n2^4 - n3^4 - 2*n1^2*n2^2 - 2*n1^2*n3^2 - 2*n2^2*n3^2 + n1^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n2^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + 2*n1^2*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n1^2*n3^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos(y)^2*sin(z)^2 + n2^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 + 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 - 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2 + 2*n1*n3^3*cos(y)*cos(z)*sin(y) - 2*n2*n3^3*cos(y)*sin(y)*sin(z) + n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n2^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n1^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2 - 2*n1*n2*n3^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(3/2) + 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(3/2) - 2*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1^3*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n2*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) - 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) + 2*n1^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n2^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 4*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z) + 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^2*n2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2))/(n1^2 + n2^2 + n3^2)^2)*abs(n3^4*sin(y)^2 - n1^4 - n2^4 - n3^4 - 2*n1^2*n2^2 - 2*n1^2*n3^2 - 2*n2^2*n3^2 + n1^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n2^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + 2*n1^2*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n1^2*n3^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos(y)^2*sin(z)^2 + n2^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 + 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 - 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2 + 2*n1*n3^3*cos(y)*cos(z)*sin(y) - 2*n2*n3^3*cos(y)*sin(y)*sin(z) + n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n2^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n1^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2 - 2*n1*n2*n3^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(3/2) + 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(3/2) - 2*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1^3*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n2*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) - 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) + 2*n1^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n2^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 4*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z) + 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^2*n2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2))^(1/2)*(1/2 + 1i/2) + n3^2*sin(y) + abs(n3^4*sin(y)^2 - n1^4 - n2^4 - n3^4 - 2*n1^2*n2^2 - 2*n1^2*n3^2 - 2*n2^2*n3^2 + n1^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n2^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + 2*n1^2*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 + n1^2*n3^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos(y)^2*sin(z)^2 + n2^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 + 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 - 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2 + 2*n1*n3^3*cos(y)*cos(z)*sin(y) - 2*n2*n3^3*cos(y)*sin(y)*sin(z) + n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n2^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 + n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + n1^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2 - 2*n1*n2*n3^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(3/2) + 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(3/2) - 2*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1^3*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n2*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) - 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) + 2*n1^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n2^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) + 4*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z) + 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) + 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^2*n2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2))^(1/2)*(1/2 - 1i/2) + n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y) + n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y) - n2*n3*cos(y)*sin(z) + n1*n3*cos(y)*cos(z) + n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z)))/(2*abs(n3^2*sin(y) - (n1^4 - n3^4*sin(y)^2 + n2^4 + n3^4 + 2*n1^2*n2^2 + 2*n1^2*n3^2 + 2*n2^2*n3^2 - n1^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 - n2^4*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 - 2*n1^2*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*sin(y)^2 - n1^2*n3^2*cos(y)^2*cos(z)^2 - n2^2*n3^2*cos(y)^2*sin(z)^2 - n2^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 - n1^4*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 - 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y)^2 + 2*n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2 - 2*n1*n3^3*cos(y)*cos(z)*sin(y) + 2*n2*n3^3*cos(y)*sin(y)*sin(z) - n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 - n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 - n2^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - n2^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)^2 - n1^2*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 - n1^2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*sin(z)^2 + 2*n1^2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2 + 2*n1*n2*n3^2*cos(y)^2*cos(z)*sin(z) + 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) - 2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(3/2) - 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) - 2*n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(3/2) + 2*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^3*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) - 2*n1^3*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1^3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) - 2*n1^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) - 2*n2*n3^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) + 2*n2^3*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) + 2*n1^2*n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3^2*sin((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1*n2^2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n2^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1^3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y) + 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z) - 2*n1^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n2^2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*cos(z)*sin(y) - 4*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z) - 2*n1^2*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)*sin(y)*sin(z) - 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1*n2*n3^2*cos((n1^2 + n2^2 + n3^2)^(1/2))^2*cos(y)^2*cos(z)*sin(z) + 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*sin(z)^2*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1^2*n2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*sin(y)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n1*n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) + 2*n1^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - 2*n2^2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)^2*cos(z)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2))^(1/2)*1i + n1^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y) + n2^2*cos((n1^2 + n2^2 + n3^2)^(1/2))*sin(y) - n2*n3*cos(y)*sin(z) + n1*n3*cos(y)*cos(z) + n2*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z)*(n1^2 + n2^2 + n3^2)^(1/2) + n1*sin((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z)*(n1^2 + n2^2 + n3^2)^(1/2) - n1*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*cos(z) + n2*n3*cos((n1^2 + n2^2 + n3^2)^(1/2))*cos(y)*sin(z))*(n1^2 + n2^2 + n3^2)^2)% must be zero!!!

Does anyone know where the mistake is?

Answer 1

isAlways(expr2 == numExpr2/denExpr2)

returns 1 (true).

Because the expression involves a number of terms, expressing it as numerator and denominator gives an expression that looks different enough from the original expression that MATLAB has a difficult time simplifying it to 0, especially working over the complex domain in combination with the abs()