This week I have been investigating the impact of perturbing the evaluation of random floating-point expressions. In particular, the impact of adding 1 (and larger values) at a random point in an expression containing many binary operators (simply some combination of add/multiply).
What mechanisms make it possible for the evaluation of an expression to be unchanged by a perturbation of +1.0 (and much larger values)? There are two possible mechanisms:
The impact of a perturbation disappears when its value is involved in a sufficiently long sequence of repeated multiplications.