itertools vs purity

[buran]

well, I don't think it is correct to compare these two. itertools.accumulate will iterate over len(a_lit) number of sums, and you a calculating just the last one.
it's correct to compare with sum

 

import itertools
import time
 
 
a_list = []
for member in range(1, 1000001):
    a_list.append(member)
list_length = len(a_list)
 
 
def accum(a_list):
    acc = itertools.accumulate(a_list)
    for n in acc:
        total = n
    print("Total from itertools = ", total)
    return
 
 
def by_formula(list_length):
    same_result = list_length * (list_length + 1) / 2
    print("\nTotal from formula = ", int(same_result))
    return

def by_sum(a_list):
    print("\nTotal from sum = ", sum(a_list))
    return
 
 
start_1 = time.time()
first = accum(a_list)
print('first took {0:0.7f} seconds'.format(time.time() - start_1))
 
start_2 = time.time()
second = by_formula(list_length)
print('second took {0:0.10f} seconds'.format(time.time() - start_2))

start_3 = time.time()
third = by_sum(a_list)
print('third took {0:0.10f} seconds'.format(time.time() - start_3))

Output:
Total from itertools =  500000500000
first took 0.0474508 seconds

Total from formula =  500000500000
second took 0.0000219345 seconds

Total from sum =  500000500000
third took 0.0085046291 seconds

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however, you can use formula, e.g. sum of arithmetic progression or geometric progression only in some cases, depending of the sequence
e.g. if the list has random numbers, formula will not help