E.g. you avoid lookup tables when you can, or only use smaller ones you know to fit in one or two SIMD registers. gcc and clang can't vevtorize it as is, but they do if you remove the brancjes than handle infinity and over/under-flow.

In the godbolt link I copied the musl expf implementation and icx was able to vectorize it, even though it uses a LUT to large for SIMD registers.

#pragma omp simd and equivalents will encourage the compiler to vectorize a specific loop and produce a warning if a loop isn't vectorized.