Personally I do a lot of approximations of math functions, which usually give me about a 10x speed increase relative to <math.h>. From the looks of it, this isn't quite that fast.
LLVM doesn't have a vector math library, so SLEEF could help you there.
If you're using single precision and AVX512, a >10x speed increase is likely. Otherwise, you'll probably get less than that. These functions are very accurate, most to withing 1 ULP of least precision. That is, if the answer they provide isn't the correctly rounded floating point answer, then it'll be either the next or previous representable floating point number.
There is a lot of room for giving up accuracy in the name of speed (eg, using less terms in the polynomials).
Sorry I wasn't clear, by "10x" I meant 10x faster than the standard library with the fastest compiler options (-O3 -ffast-math -avx512), but I've only tested with clang.