Improving performance of SEOBNRv3 by $\sim$300x

When a gravitational wave is detected by Advanced LIGO/Virgo, sophisticated parameter estimation (PE) pipelines spring into action. These pipelines leverage approximants to generate large numbers of theoretical gravitational waveform predictions to characterize the detected signal. One of the most accurate and physically comprehensive classes of approximants in wide use is the "Spinning Effective One Body--Numerical Relativity" (SEOBNR) family. Waveform generation with these approximants can be computationally expensive, which has limited their usefulness in multiple data analysis contexts. In prior work we improved the performance of the aligned-spin approximant SEOBNR version 2 (v2) by nearly 300x. In this work we focus on optimizing the full eight-dimensional, precessing approximant SEOBNR version 3 (v3). While several v2 optimizations were implemented during its development, v3 is far too slow for use in state-of-the-art source characterization efforts for long-inspiral detections. Completion of a PE run after such a detection could take centuries to complete using v3. Here we develop and implement a host of optimizations for v3, calling the optimized approximant v3_Opt. Our optimized approximant is about 340x faster than v3, and generates waveforms that are numerically indistinguishable.