Add fast_substitute

Before:
```julia
julia> @time sysRed = tearing(sysEx);
  8.903631 seconds (42.38 M allocations: 2.968 GiB, 8.06% gc time)
```

After:
```julia
julia> @time tearing(sysEx);
  1.733097 seconds (10.90 M allocations: 1.059 GiB, 19.44% gc time)
```

Author: YingboMa

src/structural_transformation/StructuralTransformations.jl

@@ -22,7 +22,8 @@ using ModelingToolkit: ODESystem, AbstractSystem, var_from_nested_derivative, Di
                        get_postprocess_fbody, vars!,
                        IncrementalCycleTracker, add_edge_checked!, topological_sort,
                        invalidate_cache!, Substitutions, get_or_construct_tearing_state,
-                       AliasGraph, filter_kwargs, lower_varname, setio, SparseMatrixCLIL
+                       AliasGraph, filter_kwargs, lower_varname, setio, SparseMatrixCLIL,
+                       fast_substitute
 
 using ModelingToolkit.BipartiteGraphs
 import .BipartiteGraphs: invview, complete

src/structural_transformation/symbolics_tearing.jl

@@ -227,7 +227,7 @@ function tearing_reassemble(state::TearingState, var_eq_matching, ag = nothing;
     idx_buffer = Int[]
     sub_callback! = let eqs = neweqs, fullvars = fullvars
         (ieq, s) -> begin
-            neweq = substitute(eqs[ieq], fullvars[s[1]] => fullvars[s[2]])
+            neweq = fast_substitute(eqs[ieq], fullvars[s[1]] => fullvars[s[2]])
             eqs[ieq] = neweq
         end
     end
@@ -282,7 +282,7 @@ function tearing_reassemble(state::TearingState, var_eq_matching, ag = nothing;
             end
             for eq in 𝑑neighbors(graph, dv)
                 dummy_sub[dd] = v_t
-                neweqs[eq] = substitute(neweqs[eq], dd => v_t)
+                neweqs[eq] = fast_substitute(neweqs[eq], dd => v_t)
             end
             fullvars[dv] = v_t
             # If we have:
@@ -295,7 +295,7 @@ function tearing_reassemble(state::TearingState, var_eq_matching, ag = nothing;
             while (ddx = var_to_diff[dx]) !== nothing
                 dx_t = D(x_t)
                 for eq in 𝑑neighbors(graph, ddx)
-                    neweqs[eq] = substitute(neweqs[eq], fullvars[ddx] => dx_t)
+                    neweqs[eq] = fast_substitute(neweqs[eq], fullvars[ddx] => dx_t)
                 end
                 fullvars[ddx] = dx_t
                 dx = ddx
@@ -655,7 +655,7 @@ function tearing_reassemble(state::TearingState, var_eq_matching, ag = nothing;
         obs_sub[eq.lhs] = eq.rhs
     end
     # TODO: compute the dependency correctly so that we don't have to do this
-    obs = substitute.([oldobs; subeqs], (obs_sub,))
+    obs = fast_substitute([oldobs; subeqs], obs_sub)
     @set! sys.observed = obs
     @set! state.sys = sys
     @set! sys.tearing_state = state

src/systems/alias_elimination.jl

@@ -151,10 +151,9 @@ function alias_elimination!(state::TearingState; kwargs...)
             k === nothing && break
         end
     end
-    subfun = Base.Fix2(substitute, subs)
     for ieq in eqs_to_update
         eq = eqs[ieq]
-        eqs[ieq] = subfun(eq.lhs) ~ subfun(eq.rhs)
+        eqs[ieq] = fast_substitute(eq, subs)
     end
 
     for old_ieq in to_expand

src/utils.jl

@@ -741,3 +741,36 @@ function jacobian_wrt_vars(pf::F, p, input_idxs, chunk::C) where {F, C}
     cfg = ForwardDiff.JacobianConfig(p_closure, p_small, chunk, tag)
     ForwardDiff.jacobian(p_closure, p_small, cfg, Val(false))
 end
+
+# Symbolics needs to call unwrap on the substitution rules, but most of the time
+# we don't want to do that in MTK.
+function fast_substitute(eq::Equation, subs)
+    fast_substitute(eq.lhs, subs) ~ fast_substitute(eq.rhs, subs)
+end
+function fast_substitute(eq::Equation, subs::Pair)
+    fast_substitute(eq.lhs, subs) ~ fast_substitute(eq.rhs, subs)
+end
+fast_substitute(eqs::AbstractArray{Equation}, subs) = fast_substitute.(eqs, (subs,))
+fast_substitute(a, b) = substitute(a, b)
+function fast_substitute(expr, pair::Pair)
+    a, b = pair
+    isequal(expr, a) && return b
+
+    istree(expr) || return expr
+    op = fast_substitute(operation(expr), pair)
+    canfold = Ref(!(op isa Symbolic))
+    args = let canfold = canfold
+        map(SymbolicUtils.unsorted_arguments(expr)) do x
+            x′ = fast_substitute(x, pair)
+            canfold[] = canfold[] && !(x′ isa Symbolic)
+            x′
+        end
+    end
+    canfold[] && return op(args...)
+
+    similarterm(expr,
+                op,
+                args,
+                symtype(expr);
+                metadata = metadata(expr))
+end