A developer has discovered a new optimization for the arcsine approximation function that delivers up to 1.8x speedup on Intel processors. The breakthrough comes from applying Estrin's Scheme to restructure the polynomial evaluation, reducing dependency chains from three to two operations. This allows modern out-of-order CPUs to execute calculations in parallel.

Initial measurements show dramatic improvements on Intel i7-10750H chips, where the optimized version runs in 41.4ms versus 48.4ms for the previous implementation. The technique particularly benefits Linux and Windows GCC/Clang compilers, though AMD Ryzen and Apple M4 chips see minimal gains. Testing across multiple environments included Ubuntu 24.04 LTS, Windows 11, and macOS Tahoe.

The optimization matters because arcsine calculations are common in computer graphics and ray tracing applications. When applied to a ray tracer benchmark, the improvement yielded a modest +3% speedup on Intel hardware. The developer emphasizes this is an approximation, not the exact arcsine function, making it suitable for most graphics applications but not all mathematical contexts.