If there are complex equations involved, it absolutely is faster. You can also create intermediate LUTs, so the tables are small and fit in cache and then do interpolation on the fly.

Not at all, when you work with DSP even nowdays using LUTs is very common and usually faster.

You are not saving a sin table, but very complex differential equations.

Yeah, isn’t hitting memory (especially if it can’t fit in L1-2 cache) one of the biggest sources of latency? Especially that on modern CPUs it is almost impossible to max out the arithmetic units, outside of microbenchmarks?