Help me figure out how much this thing fails!

pollard_failure.py

import math
import time

def f(x):
    return x**2 + 1

def pollard_rho(N):
    xn = 2
    x2n = 2
    #print("xn: {}, x2n: {}".format(xn, x2n))
    d = 1
    while d == 1:
        xn = f(xn) % N
        x2n = f(f(x2n)) % N
        #print("xn: {}, x2n: {}".format(xn, x2n))
        abs_val = abs(xn - x2n)
        d = math.gcd(abs_val, N)
    if d == N:
        return False
    else:
        return d, N//d


def calc_perc_failure():
  val = max(2, int(input("What number would you like to check up to? ")))

  success = 0
  failure = 0
  for factor in range(2, val):
      res = pollard_rho(factor)
      if not res:
          failure += 1
      else:
          success += 1

  print("Failed on {} of integers up to {}".format(failure / (success + failure), val))


while True:
  calc_perc_failure()