A method for operating on a target function to provide computer code instructions configured to implement automatic adjoint differentiation of the target function. The method comprises: determining, based on the target function, a linearized computational map (100), LCM, of the target function wherein each node of the LCM (100) comprises an elementary operation; for each node of the LCM (100) forming computer code instructions configured to: (i) compute intermediate data associated with a forward function of an automatic adjoint differentiation algorithm; and, (ii) increment, according to the automatic adjoint differentiation algorithm, adjoint variables of the preceding connected nodes of the each node in dependence on intermediate data; wherein forming computer code instructions for both step (i) and step (ii) for each node is performed prior to performing said steps for a subsequent node of the LCM (100).