from math import sqrt

N=60
eps=10**(-15)
i=0
xpp=0.1
xp=z=1.0
abserr=abs(z)

def f(x):
    return x**12-2

while i<=N and abserr>=eps*abs(z):
    z=xp-f(xp)*(xp-xpp)/(f(xp)-f(xpp))
    abserr=abs(z-xp)
    xpp=xp
    xp=z
    i=i+1
    print i,xp,abserr/abs(z),abs((xp-2**(1.0/12))/2**(1.0/12))