refactor: re-run eliminate_perfect_aliases! after alias_elimination!

[AayushSabharwal]

We run eliminate_perfect_aliases! before alias_elimination! to (significantly) reduce the number of equations the latter pass has to process. However, alias_elimination! identifies additional x ~ y equations which can easily be removed by eliminate_perfect_aliases!. This has resulted in better simplification on some models.

[oscardssmith]

Why doesn't alias_elimination! eleminate these perfect aliases?

[AayushSabharwal]

alias_elimination!, contrary to its name, doesn't actually "eliminate" anything. It just runs bariess on the equations.

[oscardssmith]

but it does have a function that runs after it to actually eliminate the aliases, right?

Also, wouldn't all of these be aliases found by adding support for the fast path detecting x~-y?

[AayushSabharwal]

but it does have a function that runs after it to actually eliminate the aliases, right?

Nope. This PR adds that.

Also, wouldn't all of these be aliases found by adding support for the fast path detecting x~-y?

I'm not sure. It's technically possible they wouldn't, but I don't know how much that would happen in practice. Once I get JuliaComputing/StateSelection.jl#81 working, I'll check if keeping this change around is worth it, since the main win from this is smaller linsolves.

[oscardssmith]

IMO the order we should go is

1. recognize x ~ -y in trivial alias detection
2. (if still useful) refactor: reduce size of inline linear solves JuliaComputing/StateSelection.jl#81
3. (if still useful) this (and if not, delete alias_elimination! if possible).

I would really like the passes we do to feel grounded and obviously correct/necessary.

[AayushSabharwal]

Yep, agreed. However, we can't delete alias_elimination! since it removes duplicate equations, which we get frequently because we allow duplicate connects (and iirc have presented MTK's ability to do so at a conference somewhere)

[oscardssmith]

I think there probably is a much simpler way to remove duplicate equations.