You might wonder why you would continue a computation if the answer is clearly wrong. IEEE arithmetic allows you to make distinctions about what kind of wrong answers can be ignored, such as NaN or Inf. Then decisions can be made based on such distinctions.
For an example, consider a circuit simulation. The only variable of interest (for the sake of argument) from a particular 50-line computation is the voltage. Further, assume that the only values that are possible are +5v, 0, -5v.
It is possible to carefully arrange each part of the calculation to coerce each sub-result to the correct range:
if computed value is greater than 4.0, return 5.0
if computed value is between -4.0 and +4.0, return 0
if computed value is less than -4.0, return -5.0
Furthermore, since Inf is not an allowed value, you need special logic to ensure that big numbers are not multiplied.
IEEE arithmetic allows the logic to be much simpler. The computation can be written in the obvious fashion, and only the final result need be coerced to the correct value—since Inf can occur and can be easily tested.
Furthermore, the special case of 0/0 can be detected and dealt with as you wish. The result is easier to read and faster in executing, since you don’t do unneeded comparisons.