I think you are confusing "proving any arbitrary algorithm is formally equivelent to another arbitrary algorithm" with "find an algorithm Y that is more efficient yet formally equivelent to algorithm X". Since we know that there are an infinite number of algorithms that are formally equivelent to any given algorithm the latter isnt such a difficult problem, especially not for a human and not when X is particularly inefficient. Also a lot of optimisation code is pretty simple in principle replacing templates that match a certain pattern with other templates that do the same thing more efficiently, and still there is no guarantee that your compilers optimizations actually work.

I think all you can do is show us what type of regexes you mean, and perhaps we can advise based on that.