Ask HN: A tool to analyse the orders of growth

You may be starting from wrong assumptions. Asymptotic analysis of algorithms is useful when you want to extrapolate to larger datasets, since it helps you figure out what, if the data grew enough, would become the bottleneck in your source code. A profiling tool is useful for getting at the actual time consumption. So what you'd want is to run your code under profiling, using a realistic amount of data. (Use a sampling profiler if the instrumented source code is too slow). Anything that looks bad at the scale that you're aiming at is something that you'd (eventually want to address). Another method would be to run the profiler twice, once on a small-ish dataset and once on a large-ish dataset (where large-ish doesn't have to be the full size) and then subtract the small-ish times (cumulative or self) from the large-ish times so you get rid of the startup time and see more clearly where the non-startup portion is spending its time.

This is a non-trivial problem, generally complexity analysis is done on paper, based on some idealised version of an algorithm. In practice implementation issues will make it difficult to extrapolate asymptotic behaviour for small n.

For instance an algorithm with O(log n) multiplications and O(n^2) additions will be dominated by the multiplications for small n, and may mislead an analysis tool into believing the asymptotic time complexity of the algorithm to be O(log n), rather than O(n^2), since the additions will dominate for very large n, simply because at some point a n^2 > m log n, where m is the run time of addition and a is the run-time of addition.

This becomes even more difficult if addition and multiplication have non-constant run-time as well (e.g. multi-precision ints).