Split the core of initdt to be algorithm independent

[ChrisRackauckas]

This should reduce precompilation

[ai-maintainer]

Generating a Review...

[topolarity]

Shaves off 10-15s of pre-compilation time on my machine (from ~4m7s)

Master trace: https://topolarity.github.io/trace-viewer/?trace=https%3A%2F%2Fraw.githubusercontent.com%2Ftopolarity%2Ftracy-traces%2Fdump%2Fdump%2Fmaster-OrdinaryDiffEq-cc46ec8b.tracy&size=2713067
With this PR: https://topolarity.github.io/trace-viewer/?trace=https%3A%2F%2Fraw.githubusercontent.com%2Ftopolarity%2Ftracy-traces%2Fdump%2Fdump%2Finit_dt_split-OrdinaryDiffEq-1328a0c3.tracy&size=2683730

Of the four-ish minutes, dominate components are:

• module-level opt/codegen (1m30s)
• per-function JIT (1m6s)
• inference (44s)
• lowering (22s)

Here are the heaviest per-function JIT hitters after this PR (in parentheses is the number of specializations):

[topolarity]

Inference time is >80% dominated by 64 specializations of solve (which later gets split into all the JIT-ed functions above):

That var"#lorenz#673" jumps out to me. Seems like we should not be specializing on the system closure function?

[ChrisRackauckas]

solve will specialize, but then internally it'll put a function wrapper on it and then it should stop specializing on it from that point?

[topolarity]

solve will specialize, but then internally it'll put a function wrapper on it and then it should stop specializing on it from that point?

I guess we'd expect future inference times for solve() with other systems to be much lower then, since they'll re-use callee results on the wrapper type (even though the entrypoint will be unique for each system)

In that case, my first-glance takeaway from the JIT list is that no single function is dominating the pre-compilation time (perform_step! is the heaviest hitter and accounts for only ~15% of the JIT time). Which means we either need to reduce the specialization N for a large number of these functions, or improve things upstream (e.g. by parallelizing this work) if we want to make a bigger dent.