The traditional method of fitting an approximate cumulative probability distribution to a data set is to bin the data in narrow bins and obtain a step function approximation. This technique suffices for many applications, but the resulting object is not a differentiable function making recovery of the underlying probability distribution function impossible. In this study, a unique group theoretic representation is used to define evolvable data warps that can be used to recover continuous, infinitely differentiable versions of the inverse cumulative distribution function. The use of a group theoretic representation permits a simple calculation to transform the evolved object into a cumulative distribution function and, via differentiation, into a probability distribution function. The group used to define the evolvable data warps is the group of bijections of the unit interval. The generators used by evolution are chosen to be differentiable in order to enable the computation of probability distribution functions. Experiments are run using a simple type of evolutionary algorithm to evolve approximate CDFs on seven data sets. The first data set is used to perform a parameter study on the representation length used to evolve the approximate CDFs and comparing two variations of the representation — one of which uses a representational control called gene expression and one of which does not.