The CORE-MATH project aims at providing opensource mathematical functions with correct rounding that can be integrated into current mathematical libraries. This article demonstrates the CORE-MATH methodology on two functions: the binary32 power function (powf) and the binary64 cube root function (cbrt). CORE-MATH already provides a full set of correctly rounded C99 functions for single precision (binary32). These functions provide similar or in some cases up to threefold speedups with respect to the GNU libc, which is not correctly rounded. This work offers a prospect of the mandatory requirement of correct rounding for mathematical functions in the next revision of the IEEE-754 standard.