I don't want to take away from his brilliance, but generally Taylor approximations perform far worse than the standard library implementations. It's also the first tool of choice for physicists, so who knows ...?
My guess, though, is that if he improved the performance, he used some other wizardry (Chebyshev or something similar).
My guess, though, is that if he improved the performance, he used some other wizardry (Chebyshev or something similar).