'''error function
erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
'''

import math

def erf(x):
    u0 = x
    u1 = -x*x*x/3.
    n = 0
    r = u0
    while abs(u0)>abs(u1):
        n += 1
        u0 = u1
        u1 = -u0*x*x*(2*n+1)/((n+1)*(2*n+3))
        r += u0
    print(n)
    return 2/math.sqrt(math.pi)*r