The problem remains if you wrap the division in a non-zero check. Or maybe the interval [-1,+1] is already kind of a lie, i.e. x is known to be in the interval

The problem remains if you wrap the division in a non-zero check. Or maybe the interval [-1,+1] is already kind of a lie, i.e. x is known to be in the interval but you additionally know that x is non-zero when you are about to perform the division. The example is just meant to illustrate the problem that using a single interval is not good enough to track error bounds in the general case.