Knuth has an entire chapter dedicated to floats, error ranges and such, which includes pretty much that (a+b)+c != a+(b+c) for floats, which in turn breaks tons

Knuth has an entire chapter dedicated to floats, error ranges and such, which includes pretty much that (a+b)+c != a+(b+c) for floats, which in turn breaks tons of things on the math side already. That is such a large issue that it has some serious consequences in the real world, e.g. constructions failing, or I remember the Patriot missile system having problems from that side.