Everyone uses math libraries. Surprisingly, mainstream math libraries do not produce correct results for several thousands of inputs. Developers are seldom aware of them, which affects reproducibility and portability. We describe our new method for synthesizing elementary functions that produces correct results for all inputs but is also significantly faster than the state of the art libraries, which have been optimized for decades.
We give an introduction to reflective towers of interpreters, a semantic model of reflection with a user level interpreted by a meta level interpreted by a meta meta level and so on.