Faster computation of $ke^{-(x – h)^2}$

The question is quite simple; almost every computer language today provides the $ \exp(x)$ function in their standard library to compute expressions like $ ke^{-(x – h)^2}.$ However, I would like to know whether this function is the fastest way to compute the above expression. In other words, is there some way to compute $ ke^{-(x – h)^2}$ faster than $ \exp(x)$ in standard libraries while keeping the result very accurate?

I would like to specify that Taylor series will not work for my application, nor will any other polynomial approximations.