We define a new, pragmatic source-code transformation algorithm for reverse-mode automatic differentiation (AD) on a significant subset of the purely functional array programming language Accelerate. The supported language subset includes standard parallel second-order array combinators but excludes sequential loops. We have a preliminary implementation of this algorithm in the Accelerate compiler that, despite being very unoptimised, comes to within an order of magnitude of state-of-the-art AD implementations. Our reverse-mode AD algorithm could generalise to other second-order, purely functional array programming languages like Futhark.