Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)?

Question

I am doing some numerical optimization on a scientific application. One thing I noticed is that GCC will optimize the call pow(a,2) by compiling it into a

Answer 1

Another similar case: most compilers won't optimize a + b + c + d to (a + b) + (c + d) (this is an optimization since the second expression can be pipelined better) and evaluate it as given (i.e. as (((a + b) + c) + d)). This too is because of corner cases:

float a = 1e35, b = 1e-5, c = -1e35, d = 1e-5;
printf("%e %e\n", a + b + c + d, (a + b) + (c + d));

This outputs 1.000000e-05 0.000000e+00