The article discusses the optimization of numerical computations through various techniques, starting from basic MLIR concepts to building a toy compiler for Python expressions. It introduces the use of the egglog library for term rewriting and optimization on Python expressions by compiling them into MLIR. The utilization of e-graphs for equality saturation, phase ordering problems, and optimization of linear algebra operations using rewrite rules is highlighted. The article explores how applying rules to NumPy expressions at compile time can lead to significant performance improvements, presenting a systematic approach to streamline numerical computations efficiently. The content also delves into the process of symbolically interpreting Python functions, converting them into an intermediate representation optimized for term rewriting and MLIR code generation.
https://vectorfold.studio/blog/egglog