A function approximation system is disclosed for determining output floating point values of functions calculated using floating point numbers. Complex functions have different shapes in different subsets of their input domain, making them difficult to predict for different values of the input variable. The function approximation system comprises an execution unit configured to determine corresponding values of a given function given a floating point input to the function; a plurality of look up tables for each function type; a correction table of values which determines if corrections to the output value are required; and a table selector for finding an appropriate table for a given function.