What essentially does ADA do?
For any given system of formulas (a model), it applies the rules of differential calculus; but numerically rather than symbolically as most people understand calculus, to produce partial derivatives of the output of the model with respect to its input parameters. Thus it is the same fundamental process that you learn in the first calculus course, but operating on numbers rather than symbols. So the results are numbers, not formulas. Formulas never exist in the process, so the whole process of algebraic manipulation is avoided by much more efficient arithmetic of differentiation.
