I don't do much float work but I don't think there is a single regular sine instruction only old x87 float stack ones.

I was curious what "sequence" would end up being but my compiler is too old for that intrinsic. Even godbolt didn't help for gcc or clang but it did reveal that icc produced a call https://godbolt.org/z/a3EsKK4aY

If you click libraries on godbolt, it's pulling in a bunch, including multiple SIMD libraries. You might have to fiddle with the libraries or build locally.