Why is 2 * x * x faster than 2 * ( x * x ) in Python 3.x, for integers?

Question

The following Python 3.x integer multiplication takes on average between 1.66s and 1.77s:

import time
start_time = time.time()
num = 0
for x in range(0, 10000000         


        

Answer 1

From what I can tell, it comes down to a little bit more memory access in the version using 2 * (x * x). I printed the disassembled bytecode and it seems to prove that:

Relevant part of 2 * x * x:

7          28 LOAD_FAST                1 (num)
           30 LOAD_CONST               3 (2)
           32 LOAD_FAST                2 (x)
           34 BINARY_MULTIPLY
           36 LOAD_FAST                2 (x)
           38 BINARY_MULTIPLY
           40 INPLACE_ADD
           42 STORE_FAST               1 (num)
           44 JUMP_ABSOLUTE           24

Relevant part of 2 * (x * x):

  7          28 LOAD_FAST                1 (num)
             30 LOAD_CONST               3 (2)
             32 LOAD_FAST                2 (x)
             34 LOAD_FAST                2 (x)
             36 BINARY_MULTIPLY                 <=== 1st multiply x*x in a temp value
             38 BINARY_MULTIPLY                 <=== then multiply result with 2
             40 INPLACE_ADD
             42 STORE_FAST               1 (num)
             44 JUMP_ABSOLUTE           24