This paper presents the method of data transformation for discovering numeric functions from their examples. Based on the idea of transformations between functions, this method can be viewed as a semantic counterpart to the more common approach of formula construction used in most previous discovery systems. Advantages of the new method include a flexible implementation through the design of transformation rules, and a sound basis for rigorous mathematical analysis to characterize what can be discovered. The method has been implemented in a discovery system called "LINUS," which can identify a wide range of functions: rational functions, quadratic relations, and many transcendental functions, as well as those that can be transformed to rational functions by combinations of differentiation, logarithm and function inverse operations.
