Task: Question Answering
Input (English): 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. 
 Question: How is correctness of automatic derivation proved?
Output (English): empirically compare automatic differentiation (AD, our implementation based on Clad) and numerical differentiation (ND, based on finite difference method)