I know that floating-point arithmetic is a bit crazy on modern computers. For example, floating-point numbers are not associative: 0.1+(0.2+0.3) = =
0.599999999999999978 (0.1+0.2)+0.3 = = 0.600000000000000089
But, at least, this is fairly consistent in my experience. You should simply not assume fancy properties like associativity to work in the real world.
Source: lemire.me