Equivalence on what metrics? In theory what you are asking for makes sense, but I think it is very hard to actually specify what equivalent means in the context of an optimization process that needs to emit code with observably different behavior. Sometimes (although admittedly rarely) speeding up sections of code can even be undesirable for example branchless code for constant time algorithms that avoid timing or energy side channel leaks, or the much more mundane elimination of signed overflow checks or other undefined behavior quirks.