Writing correct software is difficult; writing reliable numerical software involving floating-point numbers is even more difficult. Computers provide numbers with limited precision; when confronted with numbers that exceed that limit, they throw runtime exceptions or introduce approximation and error. Well-known studies (e.g., Huckle) show that numerical errors often occur and can be disastrous, even in “well-tested” code. Thus, practical techniques for systematic testing and analysis of numerical programs are much needed. In this talk, I will present my recent work on developing testing and analysis techniques for numerical software. In particular, I will introduce Ariadne, the first practical symbolic execution engine for automatically detecting floating-point exceptions, and a novel testing framework that systematically perturbs a program’s numerical calculations to elicit latent numerical instability. The tools have been extensively evaluated on the widely-used GNU Scientific Library (GSL). The results show that both tools are effective. In particular, Ariadne identified a large number of real, unchecked runtime exceptions in GSL. The GSL developers confirmed our preliminary findings and look forward to Ariadne’s imminent public release.