from math import tanh,cosh
from numpy import linspace
from pylab import plot,show

accuracy = 1e-12

def arctanh(u):
    x = 0.0
    delta = 1.0
    while abs(delta)>accuracy:
        delta = (tanh(x)-u)*cosh(x)**2
        x -= delta
    return x

upoints = linspace(-0.99,0.99,100)
xpoints = []
for u in upoints:
    xpoints.append(arctanh(u))
plot(upoints,xpoints)
show()