Example (Demmel 1984, from D. Goldberg, p. 187, adapted): In our
toy FP system let's compute

whose result is , a "normal" FP number. A direct use of the formula

returns the result equal to 0, since the denominators overflow. Using the scaled formulation

we have , and .

Sometimes overflow and infinity arithmetic mat lead to curious results.
For example, let
and compute

Since the denominator overflows it is set to infinity; the numerator does not overflow, therefore the result is !. If we compute the same quantity as

we obtain a result closer to the mathematical value.