N=30
epsilon=10**(-15)
i=0
xpp=0.5
xp=z=1.2
abserr=abs(z)
while i <= N and abserr >= epsilon*abs(z):
  z=xp-(xp**2-2.0)*(xp-xpp)/(xp**2-xpp**2)
  print i,z
  abserr=abs(z-xp)
  xpp=xp
  xp=z
  i=i+1