This is an excellent paper, describing a variant (“revolve”) of the basic form for reverse differentiation for computing the gradient of a scalar valued function, which enables computing this gradient of a function using no more than five times the number of operations needed for evaluating the function. This basic algorithm usually requires a large memory for storage of intermediate computations. The variant presented here circumvents this large memory requirement. A detailed description of the variant is given, along with motivation and proofs. The authors then illustrate the application of their algorithm to the solution of Burger’s equation.