Integration and differentiation are opposites: Integration is well behaved numerically, but poorly behaved algebraically. Differentiation is poorly behaved nu

Integration and differentiation are opposites: Integration is well behaved numerically, but poorly behaved algebraically. Differentiation is poorly behaved numerically, but well behaved algebraically. Therefore if one wants to do "automatic integration", one has to approach it in a radically different way to autodiff. And arguably, such a method does already exist; it's just very inefficient.