I originally wrote this library to er.. re-answer a stack overflow question. It has since been used for everything from analyzing high energy physics data to machine learning to computer graphics to pick and place machines to keeping flying cars aloft with people in them. The original question is at: stackoverflow.com/questions/… I first answered in the negative, then after Dan Piponi popped up with a comment, saying should be kind of possible, sweeping the asymptotics under the rug, I tied my brain into knots for ~3 days until I came up with a way to use observable sharing to get the equivalent of a classical AD"tape". Nowadays the library much more directly implements the standard tape algorithm when running in reverse mode, and relegates the weird observable sharing topological sorting variant I came up with first (now called Kahn) to the cases where users want to generate the expression spread across lots of threads/cores, and doesn't want to deal with the contention of a traditional tape. What I've always loved about this library is it makes almost no assumptions about the underlying Num instances. So you can do things like use it for symbolic computation, or even computing whole _programs_ that compute the derivatives in question, as long as the syntax tree type instantiates Num, etc. This rather greatly reduced the pressure to make it directly efficient. Whenever I wanted to use it and it wasn't directly appropriate I just applied it to an EDSL and then compiled and ran that!