A method in a network element includes processing input packets using a set of two or more functions that are defined over parameters of the input packets. Each function in the set produces respective interim actions applied to the input packets and the entire set produces respective end-to-end actions applied to the input packets. An end-to-end mapping, which maps the parameters of at least some of the input packets directly to the corresponding end-to-end actions, is cached in the network element. The end-to-end mapping is queried with the parameters of a new input packet. Upon finding the parameters of the new input packet in the end-to-end mapping, an end-to-end action mapped to the found parameters is applied to the new input packet, without processing the new input packet using the set of functions.