#!/usr/bin/python

from math import sqrt

# Get Input from User (number)
number = 16

mathlibresult = sqrt(number)

iteration = 1
newguess = number/2
difference = newguess - mathlibresult

while (difference > abs(1e-10)):
    print('Iteration: ', iteration, ' Guess: ', newguess, ' Difference: ', difference)
    oldguess = newguess
    newguess = 0.5 * (oldguess + number/oldguess)
    iteration = iteration + 1
    finaldifference = difference
    difference = newguess - mathlibresult

print('The square root from the math lib is: ',  mathlibresult)
print('The difference between math lib and Newton method is ', finaldifference)