[guyomes]

For the mantissa, the insight is probably that :

(1+e1)*(1+e2) = 1+e1+e2+(e1*e2)

If e1 and e2 are small, then e1*e2 is negligible.

[thequux]

Huh, and in the case that e1 and e2 are large, the mantissa overflows into the exponent, multiplying the result by 2.

[amelius]

I guess we're lucky that the IEEE 754 committee put the exponent in front of the mantissa. Or maybe they were aware of this trick all along ...