It's true that most autodiff systems would behave this way, but a human given only the rules of calculus (the same rules as AD) would have trouble at the same p

It's true that most autodiff systems would behave this way, but a human given only the rules of calculus (the same rules as AD) would have trouble at the same point. Of course, most mathemeticians would apply additional insights while differentiating here (such as cancellation of terms or L'Hôpital's rule). But equally, you could add these things to an AD too; they are orthogonal to the basic derivative transformation, so it's really a difference of degree at best.