A novel automated discovery approach to systematically explore IR function space.Empirical analysis of heuristic IR constraints in light of the new discovery approach.Experimental validation of effectiveness of discovered IR scoring functions. In this paper we are interested in finding good IR scoring functions by exploring the space of all possible IR functions. Earlier approaches to do so however only explore a small sub-part of the space, with no control on which part is explored and which is not. We aim here at a more systematic exploration by first defining a grammar to generate possible IR functions up to a certain length (the length being related to the number of elements, variables and operations, involved in a function), and second by relying on IR heuristic constraints to prune the search space and filter out bad scoring functions. The obtained candidate scoring functions are tested on various standard IR collections and several simple but promising functions are identified. We perform extensive experiments to compare these functions with classical IR models. It is observed that these functions are yielding either better or comparable results. We also compare the performance of functions satisfying IR heuristic constraints and those which do not; the former set of functions clearly outperforms the latter, which shows the validity of IR heuristic constraints to design new IR models.