[pkhuong]

For nice enough smooth functions, the minimax approximation can only improve Chebyshev by at most ~2 bits; this http://www.uta.edu/faculty/rcli/papers/li2004.pdf paper shows that the improvement is in fractional of bits for elementary functions. I'm really not sure it's worth the effort and incurring more error around every pole to tamp things down around Chebyshev's worst case. For single floats, I did find it interesting to restrict the search to coefficients that can be represented exactly as single floats. For doubles, rounding of coefficients is probably noise unless you're writing a libm.