It doesn't just have to be for application-specific performance though. You can also define the cost function to be to minimize the floating point error of a specific set of codes, which is what egg-herbie does. I can see throwing a custom pass on code that says "make this be the most floating point stable version it can find" as a nice quick fix for cases where application scientists without a lot of numerical analysis experience hit cases which traditionally would've required a lot more thought and care.

Another application we have in mind is to do similar linear algebra transformations to XLA. For example, sequential matrix-vector operations (A*v1 + A*v2) can be more optimally be applied as a single BLAS3 matrix-matrix call (A*[v1;v2]). Those kinds of rules can be very easily structured as an E-graph, and doing it this way would make it very inviting to mathematicians to extend and maintain the rulesets.

Both of those are cases where you may not want those passes to always be running, but they are super helpful in many numerical applications. And there's a lot more where that came from. Forward-mode AD can be implemented quite naturally this way. And there's a few more complex examples I'll hold in my back pocket until they are completed.