 Estimating the information efficiency of elementary functions is not trivial. The primitive recursive functions (see entry on  recursive functions)  have one information expanding operation, the increment operation, one information discarding operation, choosing, all the others are information neutral. The information efficiency of more complex operations is defined by a combination of counting and choosing. From an information efficiency point of view the elementary arithmetical functions are complex families of functions that describe computations with the same outcome, but with different computational histories.