I think many floating point functions (e.g. sin, cosine) are implemented using Pade rational approximations - basically, the ratio of two polynomials. (http://www.dattalo.com/technical/theory/sinewave.html)

This usually gives enough accuracy for the purposes of floating point.

However, I'm not sure if "pow" can be usefully implemented this way. I am guessing no, because pow grows faster than any polynomial eventually...

edit: Hmm, pow at least looks linear here: http://www.netlib.org/fdlibm/e_pow.c