Sadly, it is not associative (i.e. (a+b)+c != a+(b+c))
Imagine a being a large number, and b and c being so small that adding each single one to a will result in a, but adding their sum will result in just the smallest increment over a.
It's more like doing calculations on scientific notation, where there are special rules for how to keep the right number of significant figures/precision after operations. Like scientific notation, you would probably convert to one form or another (even if in your head) before doing the operation, and keep note of the possible loss of precision.
This is exactly the reason why adding floats to ints is something that people think should require an explicit conversion, so it's more obvious that's a point that may introduce loss of accuracy.
1: https://stackoverflow.com/questions/24442725/is-floating-poi...
2: https://www.cs.umd.edu/class/sum2003/cmsc311/Notes/BinMath/a...
Now that you mention, there was this fascinating denial-of-service vulnerability in PHP which is (kind of) related... https://news.ycombinator.com/item?id=2066352 http://www.exploringbinary.com/why-volatile-fixes-the-2-2250...
EDIT: To expand on this: The following code is valid, and may print "weird":
double x = f();
double y = x;
if(x != 0 && y == 0) {
printf("weird\n");
}