It depends on your model of NaN. If you think there is only one NaN value, then the two values return the same result. If there are multiple distinct NaN values

It depends on your model of NaN. If you think there is only one NaN value, then the two values return the same result. If there are multiple distinct NaN values (i.e., you distinguish between NaNs with different payloads), then the resulting payload of an arithmetic operation is... not well-specified. Most hardware architectures (x86, ARM fall into this category) pick the rule that the payload is the Nth operand (usually first, sometimes second) when multiple inputs are NaN. I believe there's some hardware where the lesser of the payloads (converted to an integer) is picked instead. RISC-V dispenses with NaN payload propagation entirely. There is theoretically the ability for hardware to generate a new unique NaN with the hardware address of the instruction into the payload, but I don't believe any hardware actually does it. Most programming languages do not generally model NaN with greater fidelity than "there is a NaN value" or maybe "there is a distinction between qNaN and sNaN."