# On the Equivalence of Automatic and Symbolic Differentiation

arXiv: https://arxiv.org/abs/1904.02990 · HTML: https://mlsanity.com/paper/1904.02990/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Information Preserving Line Search via Bayesian Optimization](https://mlsanity.com/paper/2507.15485/) (2025)
- [Differentiable Power-Flow Optimization](https://mlsanity.com/paper/2603.28203/) (2026)

## Abstract (arXiv)

We show that reverse 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.