Fix recursive structure and setup precompilation

The recursive structure of SystemStructure was giving precompilation an issue so I removed that module. Then I setup precompilation on the basic interface.  Test case:

```julia
@time using ModelingToolkit
@time using DifferentialEquations
@time using Plots
@time begin
    @variables t x(t)
    D = Differential(t)
    @nAmed sys = ODESystem([D(x) ~ -x])
end;
@time prob = ODEProblem(structural_simplify(sys), [x => 30.0], (0, 100), [], jac = true);
@time sol = solve(prob);
@time plot(sol, idxs=[x]);
```

Before:

```
11.082586 seconds (19.32 M allocations: 1.098 GiB, 4.09% gc time, 0.71% compilation time: 87% of which was recompilation)
0.639738 seconds (661.39 k allocations: 101.321 MiB, 4.33% gc time, 6.46% compilation time)
3.703724 seconds (5.71 M allocations: 322.840 MiB, 5.22% gc time, 9.92% compilation time: 86% of which was recompilation)
7.795297 seconds (8.25 M allocations: 483.041 MiB, 2.50% gc time, 99.88% compilation time)
21.719376 seconds (44.11 M allocations: 2.485 GiB, 5.68% gc time, 99.48% compilation time)
2.602250 seconds (4.04 M allocations: 253.058 MiB, 4.60% gc time, 99.90% compilation time)
2.450509 seconds (5.17 M allocations: 332.101 MiB, 5.89% gc time, 99.41% compilation time: 30% of which was recompilation)
```

After:

```
9.129141 seconds (22.77 M allocations: 1.291 GiB, 4.65% gc time, 0.62% compilation time: 87% of which was recompilation)
0.784464 seconds (667.59 k allocations: 101.524 MiB, 3.95% gc time, 4.16% compilation time)
3.111142 seconds (5.42 M allocations: 305.594 MiB, 3.82% gc time, 6.39% compilation time: 82% of which was recompilation)
0.105567 seconds (157.39 k allocations: 10.522 MiB, 8.81% gc time, 95.49% compilation time: 74% of which was recompilation)
1.993642 seconds (4.03 M allocations: 218.310 MiB, 2.69% gc time, 96.95% compilation time: 82% of which was recompilation)
1.806758 seconds (4.06 M allocations: 254.371 MiB, 4.44% gc time, 99.91% compilation time)
1.694666 seconds (5.27 M allocations: 339.088 MiB, 6.18% gc time, 99.39% compilation time: 31% of which was recompilation)
```

And that's on v1.9, so v1.10 should be even better. 20 seconds off hehe.

Author: ChrisRackauckas

ext/MTKDeepDiffsExt.jl

@@ -4,7 +4,7 @@ using DeepDiffs, ModelingToolkit
 using ModelingToolkit.BipartiteGraphs: Label,
     BipartiteAdjacencyList, unassigned,
     HighlightInt
-using ModelingToolkit.SystemStructures: SystemStructure,
+using ModelingToolkit: SystemStructure,
     MatchedSystemStructure,
     SystemStructurePrintMatrix
 

src/ModelingToolkit.jl

@@ -51,8 +51,8 @@ using PrecompileTools, Reexport
     using MLStyle
 
     using Reexport
+    using Symbolics
     using Symbolics: degree
-    @reexport using Symbolics
     using Symbolics: _parse_vars, value, @derivatives, get_variables,
         exprs_occur_in, solve_for, build_expr, unwrap, wrap,
         VariableSource, getname, variable, Connection, connect,
@@ -70,9 +70,10 @@ using PrecompileTools, Reexport
     import OrdinaryDiffEq
 
     import Graphs: SimpleDiGraph, add_edge!, incidence_matrix
-
-    @reexport using UnPack
 end
+
+@reexport using Symbolics
+@reexport using UnPack
 RuntimeGeneratedFunctions.init(@__MODULE__)
 
 export @derivatives
@@ -156,7 +157,6 @@ include("systems/dependency_graphs.jl")
 include("clock.jl")
 include("discretedomain.jl")
 include("systems/systemstructure.jl")
-using .SystemStructures
 include("systems/clock_inference.jl")
 include("systems/systems.jl")
 
@@ -172,6 +172,14 @@ for S in subtypes(ModelingToolkit.AbstractSystem)
     @eval convert_system(::Type{<:$S}, sys::$S) = sys
 end
 
+PrecompileTools.@compile_workload begin
+    using ModelingToolkit
+    @variables t x(t)
+    D = Differential(t)
+    @named sys = ODESystem([D(x) ~ -x])
+    prob = ODEProblem(structural_simplify(sys), [x => 30.0], (0, 100), [], jac = true)
+end
+
 export AbstractTimeDependentSystem,
     AbstractTimeIndependentSystem,
     AbstractMultivariateSystem

src/structural_transformation/StructuralTransformations.jl

@@ -23,14 +23,18 @@ using ModelingToolkit: ODESystem, AbstractSystem, var_from_nested_derivative, Di
     IncrementalCycleTracker, add_edge_checked!, topological_sort,
     invalidate_cache!, Substitutions, get_or_construct_tearing_state,
     filter_kwargs, lower_varname, setio, SparseMatrixCLIL,
-    fast_substitute, get_fullvars, has_equations
+    fast_substitute, get_fullvars, has_equations, observed
 
 using ModelingToolkit.BipartiteGraphs
 import .BipartiteGraphs: invview, complete
 import ModelingToolkit: var_derivative!, var_derivative_graph!
 using Graphs
-using ModelingToolkit.SystemStructures
-using ModelingToolkit.SystemStructures: algeqs, EquationsView
+using ModelingToolkit: algeqs, EquationsView,
+    SystemStructure, TransformationState, TearingState, structural_simplify!,
+    isdiffvar, isdervar, isalgvar, isdiffeq, algeqs, is_only_discrete,
+    dervars_range, diffvars_range, algvars_range,
+    DiffGraph, complete!,
+    get_fullvars, system_subset
 
 using ModelingToolkit.DiffEqBase
 using ModelingToolkit.StaticArrays

src/systems/systemstructure.jl

@@ -1,7 +1,5 @@
-module SystemStructures
-
 using DataStructures
-using Symbolics: linear_expansion, unwrap
+using Symbolics: linear_expansion, unwrap, Connection
 using SymbolicUtils: istree, operation, arguments, Symbolic
 using SymbolicUtils: quick_cancel, similarterm
 using ..ModelingToolkit
@@ -10,7 +8,7 @@ import ..ModelingToolkit: isdiffeq, var_from_nested_derivative, vars!, flatten,
     isparameter, isconstant,
     independent_variables, SparseMatrixCLIL, AbstractSystem,
     equations, isirreducible, input_timedomain, TimeDomain,
-    VariableType, getvariabletype, has_equations
+    VariableType, getvariabletype, has_equations, ODESystem
 using ..BipartiteGraphs
 import ..BipartiteGraphs: invview, complete
 using Graphs
@@ -27,8 +25,7 @@ function quick_cancel_expr(expr)
 end
 
 export SystemStructure, TransformationState, TearingState, structural_simplify!
-export initialize_system_structure, find_linear_equations
-export isdiffvar, isdervar, isalgvar, isdiffeq, isalgeq, algeqs, is_only_discrete
+export isdiffvar, isdervar, isalgvar, isdiffeq, algeqs, is_only_discrete
 export dervars_range, diffvars_range, algvars_range
 export DiffGraph, complete!
 export get_fullvars, system_subset
@@ -620,5 +617,3 @@ function _structural_simplify!(state::TearingState, io; simplify = false,
     @set! sys.observed = ModelingToolkit.topsort_equations(observed(sys), fullstates)
     ModelingToolkit.invalidate_cache!(sys), input_idxs
 end
-
-end # module

test/clock.jl

@@ -62,13 +62,12 @@ By inference:
 =>   Shift(x, 0, dt) := (Shift(x, -1, dt) + dt) / (1 - dt) # Discrete system
 =#
 
-using ModelingToolkit.SystemStructures
 ci, varmap = infer_clocks(sys)
 eqmap = ci.eq_domain
 tss, inputs = ModelingToolkit.split_system(deepcopy(ci))
-sss, = SystemStructures._structural_simplify!(deepcopy(tss[1]), (inputs[1], ()))
+sss, = ModelingToolkit._structural_simplify!(deepcopy(tss[1]), (inputs[1], ()))
 @test equations(sss) == [D(x) ~ u - x]
-sss, = SystemStructures._structural_simplify!(deepcopy(tss[2]), (inputs[2], ()))
+sss, = ModelingToolkit._structural_simplify!(deepcopy(tss[2]), (inputs[2], ()))
 @test isempty(equations(sss))
 @test observed(sss) == [yd ~ Sample(t, dt)(y); r ~ 1.0; ud ~ kp * (r - yd)]