Discontinuity modeling techniques of computing functions of a program are described. In one example, a program has a computing function that includes a discontinuity. An input is received by the data modeling system that identifies an axis. A plurality of samples is then generated by the data modeling system along the axis based on an output of the program. The samples are then used as a basis by the data modeling system to generate a data model that models the discontinuity. The data model includes, in one example, one or more gradients and models the discontinuity using a 1D box kernel.