Let's not rule out that I may just be wrong. However e-graphs are not really a general purpose thing, they're a bespoke creation for partially solving phase ord

Let's not rule out that I may just be wrong. However e-graphs are not really a general purpose thing, they're a bespoke creation for partially solving phase ordering in compilers, intermixed with the DAG tiling problem from instruction selection. Specifically, e-graphs are used with respect to an ISA from which the cost model is derived. My intuition is that this constrains the structure sufficiently that polynomial solutions can be found. Probably involving a partial order calculated ahead of time. For me, whether the result in the opening post is applicable to uses of e-graphs in compilers has a strong influence over whether I need to worry about it or not. I'm on the fence about e-graphs as a model. If rolling one into production means I'll occasionally hit exponential increases in running time as heuristics fall over, that's an argument against. If those cliffs are unreachable for a given ISA, they don't matter.