This can happen even on small systems. I once replaced a O(n^4) with O(n^2*ln(n)) on an embedded target which made a minutes long user facing process take secon

This can happen even on small systems. I once replaced a O(n^4) with O(n^2*ln(n)) on an embedded target which made a minutes long user facing process take seconds. The catch is that the original used a good algorithm, but made an implementation error which I caught in profiling. So complexity analysis is good, but the only way to get better at something is to measure it.