In this paper we propose an approach to discover functions for IR ranking from a space of simple closed-form mathematical func-tions. In general, all IR ranking models are based on two basic variables, namely, term frequency and document frequency. Here a grammar for generating all possible functions is defined which consists of the two above said variables and basic mathematical operations -addition, sub-traction, multiplication, division, logarithm, exponential and square root. The large set of functions generated by this grammar is filtered by check-ing mathematical feasibility and satisfiability to heuristic constraints on IR scoring functions proposed by the community. Obtained candidate functions are tested on various standard IR collections and several sim-ple but highly efficient scoring functions are identified. We show that these newly discovered functions are outperforming other state-of-the-art IR scoring models through extensive experimentation on several IR collections. We also compare the performance of functions satisfying IR constraints to those which do not, and show that the former set of func-tions clearly outperforms the latter one 3 .