Optimize code generated by sympy

Using SymPy to find a derivative (see this question: https://math.stackexchange.com/questions/726104/apply-chain-rule-to-vector-function-with-chained-dot-and-cross-product ), I came up with this code:

from sympy import * from sympy.physics.mechanics import * from sympy.printing import print_ccode from sympy.utilities.codegen import codegen x1, x2, x3 = symbols('x1 x2 x3') y1, y2, y3 = symbols('y1 y2 y3') z1, z2, z3 = symbols('z1 z2 z3') u = ReferenceFrame('u') u1=(u.x*x1 + u.y*y1 + u.z*z1) u2=(u.x*x2 + u.y*y2 + u.z*z2) u3=(u.x*x3 + u.y*y3 + u.z*z3) s1=(u1-u2).normalize() s2=(u2-u3).normalize() v=cross(s1, s2) f=dot(v,v) df_dy2=diff(f, y2) print_ccode(df_dy2, assign_to='df_dy2') [(c_name, c_code), (h_name, c_header)] = codegen( ("df_dy2", df_dy2), "C", "test", header=False, empty=False) print c_code

Which yields this beauty:

#include "test.h" #include <math.h> double df_dy2(double x1, double x2, double x3, double y1, double y2, double y3, double z1, double z2, double z3) { return ((x1 - x2)*(y2 - y3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - (x2 - x3)*(y1 - y2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))))*(2*(x1 - x2)*(y1 - y2)*(y2 - y3)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) + 2*(x1 - x2)*(-y2 + y3)*(y2 - y3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L)) + 2*(x1 - x2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - 2*(x2 - x3)*pow(y1 - y2, 2)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - 2*(x2 - x3)*(y1 - y2)*(-y2 + y3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L)) + 2*(x2 - x3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2)))) + (-(x1 - x2)*(z2 - z3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) + (x2 - x3)*(z1 - z2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))))*(-2*(x1 - x2)*(y1 - y2)*(z2 - z3)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - 2*(x1 - x2)*(-y2 + y3)*(z2 - z3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L)) + 2*(x2 - x3)*(y1 - y2)*(z1 - z2)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) + 2*(x2 - x3)*(-y2 + y3)*(z1 - z2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L))) + ((y1 - y2)*(z2 - z3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - (y2 - y3)*(z1 - z2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))))*(2*pow(y1 - y2, 2)*(z2 - z3)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) + 2*(y1 - y2)*(-y2 + y3)*(z2 - z3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L)) - 2*(y1 - y2)*(y2 - y3)*(z1 - z2)/(pow(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2), 3.0L/2.0L)*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - 2*(-y2 + y3)*(y2 - y3)*(z1 - z2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*pow(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2), 3.0L/2.0L)) - 2*(z1 - z2)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2))) - 2*(z2 - z3)/(sqrt(pow(x1 - x2, 2) + pow(y1 - y2, 2) + pow(z1 - z2, 2))*sqrt(pow(x2 - x3, 2) + pow(y2 - y3, 2) + pow(z2 - z3, 2)))); }

there are several multiple occurrences of the sqrts and pows of the same numbers, which could be computed once to improve readability and time of execution. But I do not know how...

Q1: Do you know of a way to make sympy do this automatically?

Q2: Do you know of a way to postprocess this code with an other tool?

Q3: Can gcc optimize this at compile time? Why?