AD has been a round since at least 1957 (the oldest reference to the class of technique I could find). When I studied it (from a CAS/PLT angle), it was considered a good middle-ground technique between symbolic methods & giving up. You can trace the result of the AD and recover a polynomial solution near the expected results (like a profile guided Taylor expansion, I guess?). It allowed us to run Buchberger's on algorithmic objects without analytic forms, and still have a chance at getting a complete basis for the antiderivative.