Mathematical modeling and simulation of complex physical systems are emerging as key technologies in engineering. Modern approaches to physical system simulation allow users to specify simulation models with the help of equation-based languages. Due to the high-level declarative abstraction of these languages program errors are extremely hard to find. This paper presents an algorithmic semi-automated debugging framework for equation-based modeling languages. We show how program slicing and dicing performed at the intermediate code level combined with assertion checking techniques can automate, to a large extent, the error finding process and behavior verification for physical system simulation models.