Specializing Python with E-Graphs

We've explored progressively more sophisticated techniques for optimizing numerical computations. We started with basic MLIR concepts, moved through memory management and linear algebra, and then neural network implementations. Each layer has added new capabilities for expressing and optimizing computations. Now we're reading to build our first toy compiler for Python expressions. In this section, we'll explore how to use the egglog library to perform term rewriting and optimization on Python expressions and compile them into MLIR. The entire source code for this section is available on GitHub. Equality Saturaiton and E-Graphs Before we dive into the implementation, let's review the key concepts of equality saturation and e-graphs. Take as an example if we have the rewrites. x * 2 → x << 1 x*y/x → y And we try to apply it over the expression (a * 2)/2 becomes (a << 1)/2 . However we should have cancelled the 2 in the numerator and denominator and got a which results in a simpler ... Read full article.