avoid differentiating expressions that are trivially zero

src/diff.jl

@@ -387,7 +387,7 @@ function executediff(D::Differential, arg::BasicSymbolic{VartypeT}; simplify=fal
                 summed_args = SymbolicUtils.ArgsT{VartypeT}()
                 sizehint!(summed_args, length(inner_args))
                 # We know `D.x` is in `arg`, so the derivative is not identically zero.
-                # `arg` cannot be `D.x` since, that would have also early exited. 
+                # `arg` cannot be `D.x` since, that would have also early exited.
                 for (i, a) in enumerate(inner_args)
                     der = derivative_idx(arr, i)::Union{Nothing, SymbolicT}
                     if isequal(a, D.x)
@@ -685,14 +685,34 @@ an array of variable expressions.
 
 All other keyword arguments are forwarded to `expand_derivatives`.
 """
+# Check if any variable in `varset` depends on `v`, either directly or
+# because it is a function whose arguments contain `v`.
+function _depends_on(varset::Set{SymbolicT}, v::SymbolicT)
+    v in varset && return true
+    for s in varset
+        if SymbolicUtils.iscall(s)
+            for arg in SymbolicUtils.arguments(s)
+                isequal(arg, v) && return true
+            end
+        end
+    end
+    return false
+end
+
 function jacobian(ops::AbstractVector, vars::AbstractVector{SymbolicT};
                   simplify=false, scalarize::Union{Val{true}, Val{false}}=Val(true), kwargs...)
     if scalarize isa Val{true}
         ops = Symbolics.scalarize(ops)
         vars = Symbolics.scalarize(vars)
     end
+    # Pre-compute variable sets to skip differentiating trivially zero Jacobian entries
+    op_varsets = Vector{Set{SymbolicT}}(undef, length(ops))
+    for i in eachindex(ops)
+        op_varsets[i] = SymbolicUtils.search_variables(ops[i])
+    end
     result = fill(COMMON_ZERO, length(ops), length(vars))
     for i in eachindex(ops), j in eachindex(vars)
+        _depends_on(op_varsets[i], vars[j]) || continue
         result[i, j] = executediff(Differential(vars[j]), ops[i]; simplify, kwargs...)
     end
     return result
@@ -921,7 +941,7 @@ function hessian(O, vars::AbstractVector; simplify=false, kwargs...)
     H
 end
 
-hessian(O, vars::Arr; kwargs...) = hessian(O, collect(vars); kwargs...) 
+hessian(O, vars::Arr; kwargs...) = hessian(O, collect(vars); kwargs...)
 
 isidx(x) = unwrap_const(x) isa TermCombination