Determine the possibility of integrating e-graphs into HEIR

I have had a vague notion for a while that e-graphs would be useful for providing a more holistic kind of rewrite engine for RLWE-level secret arithmetic on tensors and/or optimizing joint selection of linalg kernels.

Tobias Grosser and co have a paper on integrating e-graphs directly in MLIR, which would seem like a good place to start studying the extent to which using e-graphs may be well suited here.

From what I've read so far (not this paper), e-graphs suffer from performance issues, but in FHE generally, and at the layer of abstraction of secret + linalg + tensor_ext, I would hope the programs are small enough.

https://arxiv.org/abs/2505.09363