Otdfbt

@MarkusMeskanen's answer has the right bits – function calls are slow, and both genexprs and listcomps are basically function calls.

Anyway, to be pragmatic:

Using str.count(c) is faster, and this related answer of mine about strpbrk() in Python could make things faster still.

def count_even_digits_spyr03_count(n):
 s = str(n)
 return sum(s.count(c) for c in "02468")


def count_even_digits_spyr03_count_unrolled(n):
 s = str(n)
 return s.count("0") + s.count("2") + s.count("4") + s.count("6") + s.count("8")

Results:

string length: 502
count_even_digits_spyr03_list 0.04157966522
count_even_digits_spyr03_sum 0.05678154459
count_even_digits_spyr03_for 0.036128606150000006
count_even_digits_spyr03_count 0.010441866129999991
count_even_digits_spyr03_count_unrolled 0.009662931009999999

If we use dis.dis(), we can see how the functions actually behave.

count_even_digits_spyr03_for():

 7 0 LOAD_CONST 1 (0)
 3 STORE_FAST 0 (count)

 8 6 SETUP_LOOP 42 (to 51)
 9 LOAD_GLOBAL 0 (str)
 12 LOAD_GLOBAL 1 (n)
 15 CALL_FUNCTION 1 (1 positional, 0 keyword pair)
 18 GET_ITER
 >> 19 FOR_ITER 28 (to 50)
 22 STORE_FAST 1 (c)

 9 25 LOAD_FAST 1 (c)
 28 LOAD_CONST 2 ('02468')
 31 COMPARE_OP 6 (in)
 34 POP_JUMP_IF_FALSE 19

 10 37 LOAD_FAST 0 (count)
 40 LOAD_CONST 3 (1)
 43 INPLACE_ADD
 44 STORE_FAST 0 (count)
 47 JUMP_ABSOLUTE 19
 >> 50 POP_BLOCK

 11 >> 51 LOAD_FAST 0 (count)
 54 RETURN_VALUE

We can see that there's only one function call, that's to str() at the beginning:

9 LOAD_GLOBAL 0 (str)
...
15 CALL_FUNCTION 1 (1 positional, 0 keyword pair)

Rest of it is highly optimized code, using jumps, stores, and inplace adding.

What comes to count_even_digits_spyr03_sum():

 14 0 LOAD_GLOBAL 0 (sum)
 3 LOAD_CONST 1 (<code object <genexpr> at 0x10dcc8c90, file "test.py", line 14>)
 6 LOAD_CONST 2 ('count2.<locals>.<genexpr>')
 9 MAKE_FUNCTION 0
 12 LOAD_GLOBAL 1 (str)
 15 LOAD_GLOBAL 2 (n)
 18 CALL_FUNCTION 1 (1 positional, 0 keyword pair)
 21 GET_ITER
 22 CALL_FUNCTION 1 (1 positional, 0 keyword pair)
 25 CALL_FUNCTION 1 (1 positional, 0 keyword pair)
 28 RETURN_VALUE

While I can't perfectly explain the differences, we can clearly see that there are more function calls (probably sum() and in(?)), which make the code run much slower than executing the machine instructions directly.

There are a few differences that actually contribute to the observed performance differences. I aim to give a high-level overview of these differences but try not to go too much into the low-level details or possible improvements. For the benchmarks I use my own package simple_benchmark.

Generators vs. for loops

Generators and generator expressions are syntactic sugar that can be used instead of writing iterator classes.

When you write a generator like:

def count_even(num):
 s = str(num)
 for c in s:
 yield c in '02468'

Or a generator expression:

(c in '02468' for c in str(num))

That will be transformed (behind the scenes) into a state machine that is accessible through an iterator class. In the end it will be roughly equivalent to (although the actual code generated around a generator will be faster):

class Count:
 def __init__(self, num):
 self.str_num = iter(str(num))

 def __iter__(self):
 return self

 def __next__(self):
 c = next(self.str_num)
 return c in '02468'

So a generator will always have one additional layer of indirection. That means that advancing the generator (or generator expression or iterator) means that you call __next__ on the iterator that is generated by the generator which itself calls __next__ on the object you actually want to iterate over. But it also has some overhead because you actually need to create one additional "iterator instance". Typically these overheads are negligible if you do anything substantial in each iteration.

Just to provide an example how much overhead a generator imposes compared to a manual loop:

import matplotlib.pyplot as plt
from simple_benchmark import BenchmarkBuilder
%matplotlib notebook

bench = BenchmarkBuilder()

@bench.add_function()
def iteration(it):
 for i in it:
 pass

@bench.add_function()
def generator(it):
 it = (item for item in it)
 for i in it:
 pass

@bench.add_arguments()
def argument_provider():
 for i in range(2, 15):
 size = 2**i
 yield size, [1 for _ in range(size)]

plt.figure()
result = bench.run()
result.plot()

Generators vs. List comprehensions

Generators have the advantage that they don't create a list, they "produce" the values one-by-one. So while a generator has the overhead of the "iterator class" it can save the memory for creating an intermediate list. It's a trade-off between speed (list comprehension) and memory (generators). This has been discussed in various posts around StackOverflow so I don't want to go into much more detail here.

import matplotlib.pyplot as plt
from simple_benchmark import BenchmarkBuilder
%matplotlib notebook

bench = BenchmarkBuilder()

@bench.add_function()
def generator_expression(it):
 it = (item for item in it)
 for i in it:
 pass

@bench.add_function()
def list_comprehension(it):
 it = [item for item in it]
 for i in it:
 pass

@bench.add_arguments('size')
def argument_provider():
 for i in range(2, 15):
 size = 2**i
 yield size, list(range(size))

plt.figure()
result = bench.run()
result.plot()

sum should be faster than manual iteration

Yes, sum is indeed faster than an explicit for loop. Especially if you iterate over integers.

import matplotlib.pyplot as plt
from simple_benchmark import BenchmarkBuilder
%matplotlib notebook

bench = BenchmarkBuilder()

@bench.add_function()
def my_sum(it):
 sum_ = 0
 for i in it:
 sum_ += i
 return sum_

bench.add_function()(sum)

@bench.add_arguments()
def argument_provider():
 for i in range(2, 15):
 size = 2**i
 yield size, [1 for _ in range(size)]

plt.figure()
result = bench.run()
result.plot()

String methods vs. Any kind of Python loop

To understand the performance difference when using string methods like str.count compared to loops (explicit or implicit) is that strings in Python are actually stored as values in an (internal) array. That means a loop doesn't actually call any __next__ methods, it can use a loop directly over the array, this will be significantly faster. However it also imposes a method lookup and a method call on the string, that's why it's slower for very short numbers.

Just to provide a small comparison how long it takes to iterate a string vs. how long it takes Python to iterate over the internal array:

import matplotlib.pyplot as plt
from simple_benchmark import BenchmarkBuilder
%matplotlib notebook

bench = BenchmarkBuilder()

@bench.add_function()
def string_iteration(s):
 # there is no "a" in the string, so this iterates over the whole string
 return 'a' in s 

@bench.add_function()
def python_iteration(s):
 for c in s:
 pass

@bench.add_arguments('string length')
def argument_provider():
 for i in range(2, 20):
 size = 2**i
 yield size, '1'*size

plt.figure()
result = bench.run()
result.plot()

In this benchmark it's ~200 times faster to let Python do the iteration over the string than to iterate over the string with a for loop.

Why do all of them converge for large numbers?

This is actually because the number to string conversion will be dominant there. So for really huge numbers you're essentially just measuring how long it takes to convert that number to a string.

You'll see the difference if you compare the versions that take a number and convert it to a string with the one that take the converted number (I use the functions from another answer here to illustrate that). Left is the number-benchmark and on the right is the benchmark that takes the strings - also the y-axis is the same for both plots:

As you can see the benchmarks for the functions that take the string are significantly faster for large numbers than the ones that take a number and convert them to a string inside. This indicates that the string-conversion is the "bottleneck" for large numbers. For convenience I also included a benchmark only doing the string conversion to the left plot (which becomes significant/dominant for large numbers).

%matplotlib notebook

from simple_benchmark import BenchmarkBuilder
import matplotlib.pyplot as plt
import random

bench1 = BenchmarkBuilder()

@bench1.add_function()
def f1(x):
 return sum(c in '02468' for c in str(x))

@bench1.add_function()
def f2(x):
 return sum([c in '02468' for c in str(x)])

@bench1.add_function()
def f3(x):
 return sum([True for c in str(x) if c in '02468']) 

@bench1.add_function()
def f4(x):
 return sum([1 for c in str(x) if c in '02468'])

@bench1.add_function()
def explicit_loop(x):
 count = 0
 for c in str(x):
 if c in '02468':
 count += 1
 return count

@bench1.add_function()
def f5(x):
 s = str(x)
 return sum(s.count(c) for c in '02468')

bench1.add_function()(str)

@bench1.add_arguments(name='number length')
def arg_provider():
 for i in range(2, 15):
 size = 2 ** i
 yield (2**i, int(''.join(str(random.randint(0, 9)) for _ in range(size))))


bench2 = BenchmarkBuilder()

@bench2.add_function()
def f1(x):
 return sum(c in '02468' for c in x)

@bench2.add_function()
def f2(x):
 return sum([c in '02468' for c in x])

@bench2.add_function()
def f3(x):
 return sum([True for c in x if c in '02468']) 

@bench2.add_function()
def f4(x):
 return sum([1 for c in x if c in '02468'])

@bench2.add_function()
def explicit_loop(x):
 count = 0
 for c in x:
 if c in '02468':
 count += 1
 return count

@bench2.add_function()
def f5(x):
 return sum(x.count(c) for c in '02468')

@bench2.add_arguments(name='number length')
def arg_provider():
 for i in range(2, 15):
 size = 2 ** i
 yield (2**i, ''.join(str(random.randint(0, 9)) for _ in range(size)))

f, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
b1 = bench1.run()
b2 = bench2.run()
b1.plot(ax=ax1)
b2.plot(ax=ax2)
ax1.set_title('Number')
ax2.set_title('String')

All your functions contain equal number of calls to str(n) (one call) and c in "02468" (for every c in n). Since then I would like to simplify:

import timeit

num = ''.join(str(i % 10) for i in range(1, 10000001))

def count_simple_sum():
 return sum(1 for c in num)

def count_simple_for():
 count = 0
 for c in num:
 count += 1
 return count


print('For Loop Sum:', timeit.timeit(count_simple_for, number=10))
print('Built-in Sum:', timeit.timeit(count_simple_sum, number=10))

sum is still slower:

For Loop Sum: 2.8987821330083534
Built-in Sum: 3.245505138998851

The key difference between these two functions is that in count_simple_for you are iterating only throw num with pure for loop for c in num, but in count_simple_sum your are creating a generator object here (from @Markus Meskanen answer with dis.dis):

 3 LOAD_CONST 1 (<code object <genexpr> at 0x10dcc8c90, file "test.py", line 14>)
 6 LOAD_CONST 2 ('count2.<locals>.<genexpr>')

sum is iterating over this generator object to sum the elements produced, and this generator is iterating over elements in num to produce 1 on each element. Having one more iteration step is expensive because it requires to call generator.__next__() on each element and these calls are placed into try: ... except StopIteration: block which also adds some overhead.