First of all, probably your observation does not generalize well to other systems, as your way of measuring is quite unreliable because it is susceptible to fluctuation in performances that are bound to be dominated by how your OS reacts to the fluctuating system load at the time of measurement.
You should use timeit or something similar.
For example, this are the timings I get on Python 3.6 in a virtual environment (Google Colab) (which seems to be quite reproducible across the other answers):
import numba as nb
def sum_loop(n):
result = 0
for x in range(n):
result += x
return result
sum_loop_nb = nb.jit(sum_loop)
sum_loop_nb.__name__ = 'sum_loop_nb'
def sum_analytical(n):
return n * (n - 1) // 2
def sum_list(n):
return sum([x for x in range(n)])
def sum_gen(n):
return sum(x for x in range(n))
def sum_range(n):
return sum(range(n))
sum_loop_nb(10) # to trigger compilation
funcs = sum_analytical, sum_loop, sum_loop_nb, sum_gen, sum_list, sum_range
n = 1000000
for func in funcs:
print(func.__name__, func(n))
%timeit func(n)
# sum_analytical 499999500000
# 10000000 loops, best of 3: 222 ns per loop
# sum_loop 499999500000
# 10 loops, best of 3: 55.6 ms per loop
# sum_loop_nb 499999500000
# 10000000 loops, best of 3: 196 ns per loop
# sum_gen 499999500000
# 10 loops, best of 3: 51.7 ms per loop
# sum_list 499999500000
# 10 loops, best of 3: 68.4 ms per loop
# sum_range 499999500000
# 100 loops, best of 3: 17.8 ms per loop
It is unlikely that you will observe much different timings across different Python versions.
The sum_analytical() and sum_loop_nb() versions have been included just for fun and are not analyzed further.
The sum_list() is also behaving quite differently from the rest, as it is creating a large, largely unnecessary, object for the computation, and it is also not analyzed further.
The reason for these different timings is in the bytecode produced by the considered versions of the functions, of course. In particular, from sum_loop() through sum_range() one gets progressively simpler code:
import dis
funcs = sum_loop, sum_gen, sum_range
for func in funcs:
print(func.__name__)
print(dis.dis(func))
print()
# sum_loop
# 2 0 LOAD_CONST 1 (0)
# 2 STORE_FAST 1 (result)
# 3 4 SETUP_LOOP 24 (to 30)
# 6 LOAD_GLOBAL 0 (range)
# 8 LOAD_FAST 0 (n)
# 10 CALL_FUNCTION 1
# 12 GET_ITER
# >> 14 FOR_ITER 12 (to 28)
# 16 STORE_FAST 2 (x)
# 4 18 LOAD_FAST 1 (result)
# 20 LOAD_FAST 2 (x)
# 22 INPLACE_ADD
# 24 STORE_FAST 1 (result)
# 26 JUMP_ABSOLUTE 14
# >> 28 POP_BLOCK
# 5 >> 30 LOAD_FAST 1 (result)
# 32 RETURN_VALUE
# None
# sum_gen
# 9 0 LOAD_GLOBAL 0 (sum)
# 2 LOAD_CONST 1 (<code object <genexpr> at 0x7f86d67c49c0, file "<ipython-input-4-9519b0039c88>", line 9>)
# 4 LOAD_CONST 2 ('sum_gen.<locals>.<genexpr>')
# 6 MAKE_FUNCTION 0
# 8 LOAD_GLOBAL 1 (range)
# 10 LOAD_FAST 0 (n)
# 12 CALL_FUNCTION 1
# 14 GET_ITER
# 16 CALL_FUNCTION 1
# 18 CALL_FUNCTION 1
# 20 RETURN_VALUE
# None
# sum_range
# 13 0 LOAD_GLOBAL 0 (sum)
# 2 LOAD_GLOBAL 1 (range)
# 4 LOAD_FAST 0 (n)
# 6 CALL_FUNCTION 1
# 8 CALL_FUNCTION 1
# 10 RETURN_VALUE
# None