Reduce TTF@mtkmodel

[hexaeder]

This PR attemts to reduce invaldiations of @mtkmodel code and thus enables precompilation of said macro.

Still WIP, so far I've only removed invalidations on the toplevel _model_macro function, but this allready leads to a ~10s improvement in TTFX.

Below examples executed in new julia session

using ModelingToolkit
@time @eval @mtkmodel Mod begin
end;
# this PR
# 0.185190 seconds (735.61 k allocations: 37.985 MiB, 16.39% gc time, 97.47% compilation time: 91% of which was recompilation)
# master
# 16.592960 seconds (114.90 M allocations: 5.945 GiB, 9.04% gc time, 99.97% compilation time)

using ModelingToolkit
@time @eval @mtkmodel Mod begin
    @variables begin
        x(t)
        y(t)
    end
    @parameters begin
        p
    end
    @equations begin
        x ~ y + p
    end
end;
# this PR
# 12.499833 seconds (82.14 M allocations: 4.328 GiB, 9.96% gc time, 99.93% compilation time: 96% of which was recompilation)
# master
# 22.175370 seconds (121.23 M allocations: 6.330 GiB, 5.06% gc time, 99.96% compilation time: <1% of which was recompilation)

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[AayushSabharwal]

Awesome!

[hexaeder]

Hm in the end it seems all it takes is full despecialization of two recursive parser function which are very hard for the compiler.

My initial goal was to fix the invalidations (i.e. no "recompilation" on first call), but I didn't manage. However, the despecialization + precomile workload alone leads to quite the speedup...

using ModelingToolkit
@time @eval @mtkmodel Mod begin
end;
# this PR
# 0.851972 seconds (3.93 M allocations: 202.397 MiB, 4.32% gc time, 99.68% compilation time: 88% of which was recompilation)
# master
# 16.592960 seconds (114.90 M allocations: 5.945 GiB, 9.04% gc time, 99.97% compilation time)

using ModelingToolkit
@time @eval @mtkmodel Mod begin
    @variables begin
        x(t)
        y(t)
    end
    @parameters begin
        p
    end
    @equations begin
        x ~ y + p
    end
end;
# this PR
# 3.384142 seconds (5.87 M allocations: 305.992 MiB, 1.34% gc time, 99.75% compilation time: 41% of which was recompilation)
# master
# 22.175370 seconds (121.23 M allocations: 6.330 GiB, 5.06% gc time, 99.96% compilation time: <1% of which was recompilation)

@time using ModelingToolkit
@time @eval @mtkmodel Mod begin
    @constants begin
        c = 1.0
    end
    @structural_parameters begin
        structp = false
    end
    @variables begin
        x(t) = 0.0, [description="foo", guess=1.0]
    end
    @parameters begin
        a = 1.0, [description="bar"]
        if structp
            b=2*a, [description="if"]
        else
            c
        end
    end
    @equations begin
        x ~ a + b
    end
end;
# this PR
# 4.351150 seconds (7.32 M allocations: 378.812 MiB, 1.70% gc time, 99.69% compilation time: 47% of which was recompilation)
# master
# 24.336051 seconds (125.52 M allocations: 6.563 GiB, 6.53% gc time, 99.95% compilation time: <1% of which was recompilation)

[ChrisRackauckas]

Super awesome, thanks for digging into this!