You’re “hiding” an important aspect: you know that the two programs are equivalent, i.e. for all inputs they return the same output. This is something an algor

You’re “hiding” an important aspect: you know that the two programs are equivalent, i.e. for all inputs they return the same output. This is something an algorithm can’t do. If you have a given set of equivalent algorithms and you know their complexity, optimizing is somehow easier (though you can still get into complexity issues).