I guess floats are still mostly deterministic if you use the exact same machine code on every PC.
Nope, they are not. Part of the problem is that "mostly deterministic" is a synonym for "non-deterministic".
- Inconsistent use of floating-point precision, which can arise surprisingly easily if e.g. you had optional hardware acceleration support, but didn't truncate the intermediate results after every operation to match the smaller precision of the software version and other platforms.
- Treating floating-point arithmetic as associative, whether at the compiler level, the network level, or even the code level. Common violations here include: changing compiler optimization flags between versions (or similar effects from compiler bugs/changes), not annotating network messages or individual events with strictly consistent sequence numbers, and assuming it's safe to "batch" or "accumulate" deltas before applying them.
- Relying on hardware-accelerated trigonometric etc. functions, which are implemented slightly differently from FPU to FPU, since these, unlike basic arithmetic, are not strictly specified by IEEE. There are many reasons for them to vary, too, like: which argument ranges should be closest to correct, should a lookup table be used to save time or avoided to save space, after how many approximation iterations should the computation stop, etc.