The easiest way to make elementary functions faster is to use a different libm: the glibc preoccupation with being correctly rounded (ie accurate to within 0.5 ulps) imposes significant performance penalties. For example the glibc log function, which is often the dominant cost in a lot of sampling algorithms, is about 2.5x slower than a straightforward implementation (ie no fancy SIMD tricks) of Tang's 25 year old table lookup algorithm, which is accurate to 0.57 ulps. Recent OS X libms are faster still, and appear to be accurate to about 0.51 ulps, though unfortunately are closed source.