I'm sorry, you are right that it's always good to avoid redundant operations. I just wanted to point out that sqrt was not a likely bottleneck, but that the algorithm was the problem (and in that we agree). By avoiding sqrt you might get a size-independent 5% percent improvement if you are lucky, but by using a better algorithm you get a 99% improvement for sufficiently large systems if you have N^1 scaling instead of N^2 (note: by improvement I mean reduction in execution time).