erf_stand_alone(x) implementation is based on formula 7.1.26 from . The maximum error is below 1.5 * 10-7.
The formula  appears as 1 – (a1 t^1 + a2 t^2 + a3 t^3 + a4 t^4 + a5 t^5) exp(-x^2), which is absolutely correct. But directly evaluating an nth order polynomial takes O(n^2) operations, while the factorization used in the code above uses O(n) operations. This technique is known as Horner’s method.
 Milton Abramowitz and Irene A. Stegun. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Vol. 55. Courier Corporation, 1964. Formula 7.1.26.
Giacomo Alessandroni (2021). Error function stand alone (https://www.mathworks.com/matlabcentral/fileexchange/55749-error-function-stand-alone), MATLAB Central File Exchange. Retrieved .
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