[Siegmund]

I should mention, in passing, that the "|hdw| + |wdh|" formulation is not completely unknown. It measures maximum possible error, if everything is off in the worst possible direction at once. You'll see this in computer science, not in statistics: that kind of analysis has to be done to guarantee that a program using floating-point operations to do large-integer arithmetic always gives the correct answer, for example.

The usual squared-uncertainties formulation, as already noted, is based on the assumption that each error is independent.