To me, trying to handle exceptions every time a NaN shows up sounds like it's riskier to performance than a few checks at important places. You wouldn't scan. Probably depends on code base.

> That does however seem strange - X was never set by operation NNNN, Y was.

If you're using NaN payloads, it would almost never be helpful for 95% of your NaNs to turn into a generic "used a NaN in arithmetic" version.