(12C) Error Function Approximation

[Albert Chan]

From Abramowitz & Stegun, 7.1.22, erf and cdf are related.

cdf(z) = (1 + erf(z/√(2)) / 2
erf(z) = 2 cdf(√(2) z) - 1 = 1 - 2 cdf(-√(2) z)

Confirm with Casio FX-115ES, R(z) = cdf(-z)

erf(0.5) = 1 - 2 R(√(2) * 0.5) = 0.5205
erf(1.6) = 1 - 2 R(√(2) * 1.6) = 0.976348
erf(2.3) = 1 - 2 R(√(2) * 2.3) = 0.9988567

Casio's Q(z) (pdf area 0.5 to z) is simpler, but not as accurate.

2 Q(√(2) * 0.5) = 0.5205
2 Q(√(2) * 1.6) = 0.97634
2 Q(√(2) * 2.3) = 0.99886