[nayuki]

Excellent article; it's very detailed in the mathematical explanations and code.

I was interested in the exponential function too, but approached it from the standpoint of arbitrary-precision arithmetic. My explanation is an order of magnitude shorter, but of course my code is a lot slower than a typical floating-point algorithm. I offer a way to compute correctly rounded exponentials without resorting to a big math package like Mathematica/Maple/etc. https://www.nayuki.io/page/approximating-eulers-number-corre...