We show that forward mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that symbolic differentiation suffers from "expression swell" whereas automatic differentiation does not. Here, we show that this statement is not true. "Expression swell" refers to the phenomenon of a much larger representation of the derivative as opposed to the representation of the original function.

翻译：我们发现,前方模式自动区别和象征性区别等同,因为它们在计算衍生物时都执行同样的操作,这与它们大相径庭的共同主张形成鲜明对照。这种区别常常通过声称象征性区别有“表情膨胀”而自动区别并不明显来说明。在这里,我们证明这种说法不真实。“表情膨胀”是指衍生物代表比最初功能代表大得多的现象。