Err... sorry... bumping once in each of the directions is linear in the number of dimensions, not exponential. You don't bump all combinations, just one dimens

Err... sorry... bumping once in each of the directions is linear in the number of dimensions, not exponential. You don't bump all combinations, just one dimension at a time. In any case, the savings from automatic differentiation are often significant, but not exponential, unless you're doing something very wrong.