Compare order of operations with wdiv and wmul

compare.py

from random import seed
from random import random

NUMBER_OF_SIMS = 100_000
TOKEN_AMOUNT_MIN = 0
TOKEN_AMOUNT_MAX = 10 ** 26

"""
  uint256 inkAtEnd = uint256(artIn).wdiv(auction_.art).wmul(auction_.ink);
"""

def wmul(x, y):
  """
        function wmul(uint256 x, uint256 y) internal pure returns (uint256 z) {
          z = x * y;
          unchecked { z /= 1e18; }
      }
  """
  z = x * y
  z = z // 10 ** 18
  return z

def wdiv(x , y):
  """
      function wdiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = (x * 1e18) / y;
    }
  """
  z = x * 10 ** 18 // y
  return z


def simulation():
  artIn = int(random() * TOKEN_AMOUNT_MAX) + TOKEN_AMOUNT_MIN
  art = int(random() * TOKEN_AMOUNT_MAX) + TOKEN_AMOUNT_MIN
  ink = int(random() * TOKEN_AMOUNT_MAX) + TOKEN_AMOUNT_MIN

  total = artIn + art + ink
  
  ## uint256 inkAtEnd = uint256(artIn).wdiv(auction_.art).wmul(auction_.ink);
  inkAtEnd_code = wmul(wdiv(artIn, art), ink)

  ## uint256 inkAtEnd = uint256(artIn).wmul(auction_.ink).wdiv(auction_.art);
  inkAtEnd_reverse = wdiv(wmul(artIn, ink), art)

  inkAtEnd_python = int(artIn * ink / art)

  diff = inkAtEnd_code - inkAtEnd_python
  diff_hypothetical = inkAtEnd_reverse - inkAtEnd_python
  diff_of_methods = inkAtEnd_code - inkAtEnd_reverse

  ## Extra logs for small sims
  if (NUMBER_OF_SIMS < 11):
    print("diff")
    print(diff)
    
    print("diff_hypothetical")
    print(diff_hypothetical)

    print("diff_of_methods")
    print(diff_of_methods)

    print("python_diff")
    print(diff - diff_hypothetical)

  diff_of_diffs = diff_of_methods

  return diff_of_diffs

def main():
  counter = 0
  relative_cumulative = 0
  for x in range(NUMBER_OF_SIMS):
    dust = simulation()
    if dust != 0:
      counter += 1
      relative_cumulative += dust

  
  print("counter")
  print(counter)

  print("relative_cumulative")
  print(relative_cumulative)

  print("avg relative cumulative")
  print(relative_cumulative / NUMBER_OF_SIMS)

  print("As % of 1e18")
  print(relative_cumulative / NUMBER_OF_SIMS / 10 ** 18 * 100)