It would be an interesting project to take in some (small) source program, and try all sorts of algebraic rearrangements (maybe just associativity and commutativity of addition and multiplication) to see if there is any noticeable performance change.

STOKE, a stochastic superoptimizer, is pretty interesting in this context: http://stoke.stanford.edu/ & https://github.com/StanfordPL/stoke

the performance definitely varies doing this by hand - I guess the current optimizers don't rearrange the code as much as a human can while seeing that it's still equivalent. But sometimes (I'm using LLVM) just rearranging the parentheses to force a different evaluation order makes a difference where I thought it wouldn't have after optimization.

This seems to be the case in 6.1 but not in 5.4. What this proves is also that this tool is really useful to check easily between gcc versions without installing all compilers /toolchains