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Explore a groundbreaking approach to rewrite rule inference in equality saturation with this 15-minute conference talk from OOPSLA 2023. Delve into Enumo, a new domain-specific language for programmable theory exploration that addresses the challenges of developing high-quality rulesets. Learn how Enumo's core operators enable strategic guidance of rule inference and incremental ruleset construction, scaling to infer deeper rules from larger grammars than previous methods. Discover the innovative fast-forwarding strategy that expands the scope of rule inference to new domains. Examine Enumo's performance across various domains, comparing it to state-of-the-art techniques and manually-developed rulesets in equality saturation-driven systems. Gain insights into the potential of this composable and scalable approach for optimizing compilers, synthesizers, and verifiers.