What I meant to say was, "If it's all in one C++ project, it's not symbolic differentiation" and I took the liberty of changing "not symbolic" to "numeric."
Having now read your posted code, I kind of feel like a 17th century naturalist trying to classify a platypus. Clearly this technique is not symbolic differentiation, since it can only produce numerical and not symbolic results (although I suppose the Jet template could handle an "expression" type as its first argument - have you actually tried this?), and it's not really numerical in the normal sense because there's no h parameter that changes the accuracy as it varies.
As an aside, "autodmatic ifferentiation" is a terrible name, in the sense that it doesn't convey any real information about the technique, except maybe that it's being done by a computer and I knew that already. It might still be a good marketing term (like how Richard Bellman named his technique "Dynamic Programming" because it's impossible to call something "dynamic" in a perjorative sense, although there really isn't anything intrinsically dynamic, and in fact you commonly end up solving "static dynamic programming" problems).