I was fiddling around with `id` recently and realized that (c?)Python does something quite sensible: it ensures that small ints always have the same `id`. 

```
>>> a, b, c, d, e = 1, 2, 3, 4, 5
>>> f, g, h, i, j = 1, 2, 3, 4, 5
>>> [id(x) == id(y) for x, y in zip([a, b, c, d, e], [f, g, h, i, j])]
[True, True, True, True, True]

```

But then it occurred to me to wonder whether the same is true for the results of mathematical operations. Turns out it is:

```
>>> nines = [(x + y, 9) for x, y in enumerate(reversed(range(10)))]
>>> [id(x) == id(y) for x, y in nines]
[True, True, True, True, True, True, True, True, True, True]

```

Seems like it starts failing at n=257...

```
>>> a, b = 200 + 56, 256
>>> id(a) == id(b)
True
>>> a, b = 200 + 57, 257
>>> id(a) == id(b)
False

```

But sometimes it still works even with larger numbers:

```
>>> [id(2 * x + y) == id(300 + x) for x, y in enumerate(reversed(range(301)))][:10]
[True, True, True, True, True, True, True, True, True, True]

```

What's going on here? How does python do this?