[pclmulqdq]

A 6th degree polynomial is firmly in the "fast approximation" category. I think sin/cos are ~15th degree polynomials for 1 ULP of precision.

[adgjlsfhk1]

sin/cos commonly use 2 different 5th degree polynomials (depending on quadrant of the sin graph) https://github.com/JuliaLang/julia/blob/bb83df1d61fb649efd15...

[moonchild]

https://github.com/rutgers-apl/The-RLIBM-Project/blob/main/l... has a lot less and claims to be correctly rounded.

[pclmulqdq]

For 32-bit float, yes. For double precision, not so much.