A more direct link to a list of applications of egraphs is https://egraphs-good.github.io/ Largely optimizing rewrites in compilers/synthesizers/query optimizer and theorem proving applications.
How does egglog compare to bddbddb, a Datalog engine powered by BDDs?
They use BDDs in Datalog to solve previously unsolved problems like context-sensitive pointer analysis for large programs and show that analyses implemented with it are faster than hand-tuned implementations and use dramatically fewer lines of code.
The egglog repo is here https://github.com/mwillsey/egg-smol with a wasm compiled web demo with examples here https://www.mwillsey.com/egg-smol/
It is still in pre-release, so there are no guarantees of stability and not necessarily ready for people to pile in.
This system is related to ones Yihong Zhang and I gave separate talks on at last year EGRAPHS 2022 workshop https://effect.systems/doc/pldi-2022-egraphs/abstract.pdf http://www.philipzucker.com/egglog/