E-graphs are interesting, but one still has to deal with combinatorial explosions. Are you alluding to some powerful search heuristic?
Your example touches on the problems of inflexible ABI, namely caller saved registers and the unknowability of side effects of external functions. Very weird that it can't reorder `r = x+y` despite it having no "observable" side effect until `return r`, since that return dominates the assignment, and there's no real relation between (the return, assignment) and (eff()).
I looked at it closer. In C, it is a side effect to assign to a variable. For an extern function not annotated __attribute__((pure)) the compiler has to assume the function call generates side effects. This prevents it from reordering the assignment and function call. Since x86-64 ABI has caller saved registers, in the case where it calls eff() first, it has to save x and y, and after the call, restore them.
My example has nothing whatsoever to do with abi, and everything to do with ir. f and g are exactly semantically equivalent, and this equivalence is trivial to show; that the compilers generate different code for each demonstrates redundancies in their ir.
Your example touches on the problems of inflexible ABI, namely caller saved registers and the unknowability of side effects of external functions. Very weird that it can't reorder `r = x+y` despite it having no "observable" side effect until `return r`, since that return dominates the assignment, and there's no real relation between (the return, assignment) and (eff()).