Approximation of the error function, $${\rm erf}(z) = \frac{2}{\sqrt{\pi}}\int_{-\infty}^{z}\!{\rm d}x\,{\rm e}^{-x^2},$$ using elementary functions could be useful, particularly for PDC and spatial walk-off  simulations…
Wikipedia, Sergei Winitzki’s paper

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Erf function approximation
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