IEEE-754 doesn't mandate exact results for functions like exp(x). It mandates things like "within 2 ULP of the true answer." Hardware vendors are free to implement these functions in any way that meets the error tolerance.

Batching order, as you mentioned, matters a lot, and for any heavily optimized kernels it will change from one machine to the next. You also have the choice of backend numerical library from, e.g., different OS versions. There are floating-point bugs from time to time, especially in GPUs. Many operations (like transcendentals) are usually given a couple bits of wiggle room in the result. Another program executing could have changed the floating-point rounding mode on one device. More aggressive ML optimizers might automatically apply various forms of reduced precision to the requested high-level operation. If you have enough optimizations enabled, you might non-deterministically get compiled instructions like fmadd so that any one build of your library is deterministic (excluding other ideas mentioned above) but different machines with different builds (because of a staged rollout, different architectures, engineering mistakes, etc) can have different outputs. And so on.

While the IEEE 754 standard ensures that individual basic operations are deterministic and strictly bounded, it does not guarantee that an entire program will yield bit-identical results on all CPUs.

CPUs and their execution environments introduce subtle hardware variations, architecture choices, and compiler optimizations that break bit-level consistency.

(same for GPU/TPU, ...)