1. A computer implemented method for verifying error tolerances of a numerical operation, the method comprising: receiving a finite precision definition for an approximation of an infinite precision numerical function, wherein the infinite precision numerical function is implemented in a processor design under test in a form of a polynomial of bounded functions; receiving a domain for verifying outputs of segments associated with the infinite precision numerical function; splitting the domain into at least two segments, wherein each segment is non-overlapping with any other segment; converting, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment among the at least two segments; calculating, for each segment, an upper bound of the polynomial for the at least two segments, beginning with the selected segment; and reporting the segments that violate a bounding condition, wherein splitting, converting and calculating are performed by a processor.