A math library implementor will generally be familiar with at least minimax and Chebyshev approximations, and generally Padé and Carathéodory-Fejér approximatio

A math library implementor will generally be familiar with at least minimax and Chebyshev approximations, and generally Padé and Carathéodory-Fejér approximations as well. (Source: I implemented math libraries for a decade. We used all of these frequently.)