Rejection Sampling's Unexpected Triumph: A Deep Dive into Performance Testing

While optimizing his ray tracer, PSRayTracing, the author delved into performance testing for algorithms generating random vectors within a unit circle/sphere. Initially, he believed an analytical solution would be more efficient than rejection sampling. However, benchmarks in Python and C++, across various compilers and hardware platforms, yielded surprising results: with compiler optimizations enabled, rejection sampling often outperformed the analytical approach. The author concludes that practical performance testing is crucial when optimizing code, avoiding reliance on theoretical assumptions, as compiler optimization strategies and hardware variations significantly impact final performance.