You should never assume the compiler is allowed to reorder floating-point computations like it does with integers. Integer math is exact, within its domain. Floating-point math is not. The IEEE-754 standard knows this, and the compiler knows this.
Ah, fair point, it has been a while since I've needed fast inexact math.
Though... they are allowed to cache common subexpressions, and my point about dependency chains is quite relevant on modern hardware. So x*x, x*x*x, etc may each be computed once. And since arithmetic operators are left-to-right associative, the rather ugly code, as written, is fast and not as wasteful as it appears.
> And since arithmetic operators are left-to-right associative, the rather ugly code, as written, is fast and not as wasteful as it appears.
This is incorrect, for exactly the reason you are citing: A * x * x * x * x = (((A * x) * x) * x) * x), which means that (x * x) is nowhere to be seen in the expression and cannot be factored out. Now, if you wrote x * x * x * x * A instead, _then_ the compiler could have done partial CSE against the term with B, although still not as much as you'd like.
