The standard normal cumulative distribution function (CDF), often written Φ(x), is closely related to the error function erf(x) but is more common than the latter in statistical applications. See these notes on how the two functions are related.
The following code computes Φ(x) in pure Haskell with no external dependencies.
phi :: Double -> Double phi x = y where a1 = 0.254829592 a2 = -0.284496736 a3 = 1.421413741 a4 = -1.453152027 a5 = 1.061405429 p = 0.3275911 -- Abramowitz and Stegun formula 7.1.26 sign = if x > 0 then 1 else -1 t = 1.0/(1.0 + p * abs x / sqrt 2.0) e = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*exp(-x*x/2.0) y = 0.5*(sign*e + 1.0) test_phi :: Bool test_phi = maximum [ abs(phi x - y) | (x, y) <- zip xs ys ] < epsilon where epsilon = 1.5e-7 -- accuracy promised by A&S xs = [-3, -1, 0.0, 0.5, 2.1 ] ys = [0.00134989803163, 0.158655253931, 0.5, 0.691462461274, 0.982135579437]