Profiling doesn't mean you don't do the math. Profiling is simply there to show you that "hey, this is where the problems actually are". You do profiling beca

Profiling doesn't mean you don't do the math. Profiling is simply there to show you that "hey, this is where the problems actually are". You do profiling because it's WAY too easy to get obsessed about theoretical problems when a simple measurement will show you the actual problems. You do the math on the actual problem location, not a method with O(n!) which only gets called with n=3. You still have to look at the entire call stack when profiling (which means thinking about the overarching algorithm).