The systems biology markup language (SBML) permits to represent biological models mixing reaction networks, algebraic equations, differential equations, and events. Its main objective is to exchange biological models between various tools for simulation and analysis. The specification of SBML, however, lacks a formal semantics. This makes it often difficult to understand SMBL models and to design correct and general interfaces with SBML. In the present paper, we propose Core SBML, a novel language covering a large subset of SBML with clear formal semantics.We present a compiler of the delay-free fragment of SBML to Core SBML (without any formal correctness guarantees). We then show how to compile Core SBML further to BioCham while preserving the semantics. We implemented and applied our compilers to the more than 500 SBML models from the curated part of the BioModels database.