Crash due to division by zero? How about multiplication by zero?

I recently transferred to the next level of floating point arithmetic caveats. Division by zero is something we all know about, but multiplication by zero can be as harmful.

An algorithm computed weight of entities, then converted them to integers, as in

This code may fail the assertion. Imagine y is large (say, 1000), so exp(y) no longer fits double. The value of exp(y) will be +Infinity in this case. Surprisingly, it will correctly understand that INT_MAX is less than +Infinity, and will pass the check as expected. But here's when multiplication by zero kicks in.

What will happen if x is 0, and exp(y) is infinity? Any result will be mathematically nonsense, unless it's a special value of "Not A Number". min() would also return NaN, and integer conversion will happily convert it to... -2147483648. The assertion fails, and the production job crashes because it does not expect the result to be negative. We're multiplying two positive floating point numbers, how can it be negative?

Yet it is. All because of multiplication by zero.