[titzer]

No, they consistently perform optimizations that violate IEEE 754 rules, such as reassociation and commutation of expressions. These are difficult to observe (unless you are in the habit of observing -0 vs 0), but yes, you can observe them. They are very precisely specified by IEEE 754 and C/C++ compilers perform illegal optimizations.

[jcranmer]

They do those optimizations when you enable fast-math flags. Some compilers (e.g., icc) enable those by default. When fast-math is not enabled, then the IEEE 754-violating optimizations are disabled.

Source: I've been working on such optimizations this past week. And that means establishing precisely which flags I need to have enabled in order for optimization to kick in.

[zaitanz]

This is very true. Once upon a time -o3 would enable fast-math. We're very careful to ensure we use test models to verify the outputs of release binaries. Enabling fast-math as you have said optimises the equations in a way that produces different results.