Apologies if the question is too elementary here.

For a certain computational application I need to approximate Gaussian distribution $e^{-x^2}$ with specific absolute precision (within $10^{-7}$ over $\mathbb{R}$), preferably with rational functions.

Alas, I'm not familiar with approximation theory. Google pointed me toward Pade approximation as the way to go. Alas, I still don't know how to derive Pade approximation for a given function, much less how to ensure the approximation would fit to the prescribed precision. Could you point me towards the relevant information?