N=40           # Max number of iterations
eps=10**(-10)
xp=z=1.2
xpp=0.5
abserr=abs(z)
i=0
while i<N and abserr>=eps*abs(z):
    z=xp-(xp-1)**3*(xp-xpp)/((xp-1)**3-(xpp-1)**3)
    abserr=abs(z-xp)
    xpp=xp
    xp=z
    i=i+1
    print 'Iteration: ', i, 'Estimate: ', xp
    print '  Estimated relative error: ', abserr/abs(xp)
    print '  Exact relative error: ', abs(xp-1)
print xp