Implement the Python's `pow(...)` function as efficient as possible

pow.py

import time

def power(base, exp):
  """Implement the `pow(...)` function recursively."""
  # Base case.
  if exp == 0:
    return 1
  elif exp == 1:
    return base
  # Compute: a^b = a^(c+d) = (a^c) * (a^d)
  if exp % 2 == 0:  # when even, c==d
    half = exp / 2
    return power(base, half) * power(base, half)
  else:
    c = int(exp / 2)
    d = c + 1
    return power(base, c) * power(base, d)
 

def pow_eff(base, exp):
  """Compute the `pow(...)` function more efficiently."""
  number = 1
  while exp:
    if exp & 1:
      number *= base
    exp >>= 1
    base *= base
  return number

def test(base, exp):
  """Test to compare Python's `pow(...)` with the above implementations."""
  # Test the recursive `power(...)` function.
  start = time.time()
  re_result = power(base, exp)
  re_time = time.time() - start
  
  # Test the efficient `pow_eff(...)` function.
  start = time.time()
  ef_result = pow_eff(base, exp)
  ef_time = time.time() - start
  
  # Test the Python's `pow(...)` function.
  start = time.time()
  py_result = pow(base, exp)
  py_time = time.time() - start
  
  # Print the 3 results & benchmarks.
  print(f'Rec: pow({base}, {exp}) = {re_result:,}\tTime: {re_time:.6f}')
  print(f'Eff: pow({base}, {exp}) = {re_result:,}\tTime: {ef_time:.6f}')
  print(f'Py : pow({base}, {exp}) = {re_result:,}\tTime: {py_time:.6f}')
  print('==============================================\n')
  
if __name__ == '__main__':
  # Test 1
  test(base=-2, exp=3)
  
  # Test 2
  test(base=-3, exp=2)
  
  # Test 3
  test(base=3, exp=12)
  
  # Test 4
  test(base=2, exp=16)