E-graphs are a data structure for equational reasoning and optimization over ground terms. One of the benefits of e-graph rewriting is that it can declaratively handle useful but difficult to orient identities like associativity and commutativity (AC) in a generic way. However, using these generic mechanisms is more computationally expensive than using bespoke routines on terms containing sets, multi-sets, linear expressions, polynomials, and binders. A natural question arises: How can one combine the generic capabilities of e-graph rewriting with these specialized theories? This talk discusses a pragmatic approach to this e-graphs modulo theories (EMT) question using two key ideas: bottom-up e-matching and semantic e-ids.

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