Detailed Instructions: In this task, you will be presented with a context from an academic paper and you have to write an answerable question based on the context. Your questions can be extractive, abstractive, or yes-no questions.
Q: In this section, we empirically compare automatic differentiation (AD, our implementation based on Clad) and numerical differentiation (ND, based on finite difference method) in ROOT. We show that AD can drastically improve accuracy and performance of derivative evaluation, compared to ND.
A:
How is correctness of automatic derivation proved?