Why does changing the sum order returns a different result?

2022-03-10

An answer to this question on Stack Overflow.

Question

Why does changing the sum order returns a different result?

23.53 + 5.88 + 17.64 = 47.05

23.53 + 17.64 + 5.88 = 47.050000000000004

Both Java and JavaScript return the same results.

I understand that, due to the way floating point numbers are represented in binary, some rational numbers (like 1/3 - 0.333333...) cannot be represented precisely.

Why does simply changing the order of the elements affect the result?

Answer

To add a different angle to the other answers here, this SO answer shows that there are ways of doing floating-point math where all summation orders return exactly the same value at the bit level.