An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, e-graphs remain unspecialized for this newer use case. Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites. This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation. A new amortized invariant restoration technique called rebuilding takes advantage of equality saturation's distinct workload, providing asymptotic speedups over current techniques in practice. A general mechanism called e-class analyses integrates domain-specific analyses into the e-graph, reducing the need for ad hoc manipulation. We implemented these techniques in a new open-source library called egg. Our case studies on three previously published applications of equality saturation highlight how egg's performance and flexibility enable state-of-the-art results across diverse domains.

DNA promises to be a high density data storage medium, but physical storage poses a challenge. To store large amounts of data, pools must be physically isolated so they can share the same addressing scheme. We propose the storage of dehydrated DNA spots on glass as an approach for scalable DNA data storage. The dried spots can then be retrieved by a water droplet using a digital microfluidic device. Here we show that this storage schema works with varying spot organization, spotted masses of DNA, and droplet retrieval dwell times. In all cases, the majority of the DNA was retrieved and successfully sequenced. We demonstrate that the spots can be densely arranged on a microfluidic device without significant contamination of the retrieval. We also demonstrate that 1 TB of data could be stored in a single spot of DNA and successfully retrieved using this method.

Recent program synthesis techniques help users customize CAD models (e.g., for 3D printing) by decompiling low-level triangle meshes to Constructive Solid Geometry (CSG) expressions. Without loops or functions, editing CSG can require many coordinated changes, and existing mesh decompilers use heuristics that can obfuscate high-level structure.This paper proposes a second decompilation stage to robustly łshrinkž unstructured CSG expressions into more editable programs with map and fold operators. We present Szalinski, a tool that uses Equality Saturation with semanticspreserving CAD rewrites to efficiently search for smaller equivalent programs. Szalinski relies on inverse transformations, a novel way for solvers to speculatively add equivalences to an E-graph. We qualitatively evaluate Szalinski in case studies, show how it composes with an existing mesh decompiler, and demonstrate that Szalinski can shrink large models in seconds.

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