We present an application of learning-based testing to the problem of automated test case generation (ATCG) for numerical software. Our approach uses n-dimensional polynomial models as an algorithmically learned abstraction of the SUT which supports n-wise testing. Test cases are iteratively generated by applying a satisfiability algorithm to first-order program specifications over real closed fields and iteratively refined piecewise polynomial models. We benchmark the performance of our iterative ATCG algorithm against iterative random testing, and empirically analyse its performance in finding injected errors in numerical codes. Our results show that for software with small errors, or long mean time to failure, learning-based testing is increasingly more efficient than iterative random testing.