Incorrect result of calculating the sum of two float values

[IBelolipetskij]

Bug report

There is a couple of float type values which sum turns out to be incorrect. It is enough to execute the following code:
print(12.566370614359172 + 28.274333882308138)
The resualt is 40.840704496667314 instead of 40.840704496667310. Attention should be paid to the lower digit of the value (4 vs 0)

Additionally:
For the first time, this behavior was detected on Python 3.9.13 and 3.10.5 for windows.

Your environment

• CPython versions tested on: 3.10.5+
• Operating system and architecture: Ubuntu 20.04.4 LTS

[ericvsmith]

You've exceeded the precision of double precision floating point numbers, which python uses for floats. Using exact integer multiplication and addition, but floating point division, you're seeing this:

>>> (12.566370614359172).as_integer_ratio()
(884279719003555, 70368744177664)
>>> (28.274333882308138).as_integer_ratio()
(7958517471031995, 281474976710656)
>>> (884279719003555*281474976710656 + 70368744177664*7958517471031995) / (70368744177664*281474976710656)
40.840704496667314

https://docs.python.org/3/tutorial/floatingpoint.html more or less explains what's going on.