diff --git a/src/ExpressionGraph.jl b/src/ExpressionGraph.jl
index 60519d5b..16adf00b 100644
--- a/src/ExpressionGraph.jl
+++ b/src/ExpressionGraph.jl
@@ -230,19 +230,19 @@ function find_term(a::Node)
     return term, constant
 end
 
-function matching_terms(lchild, rchild)
-    if lchild === rchild
-        return (1, 1, lchild)
-    else
-        lterm, lconstant = find_term(lchild)
-        rterm, rconstant = find_term(rchild)
-        if lterm !== nothing && rterm !== nothing && lterm === rterm
-            return (lconstant, rconstant, lterm)
-        else
-            return nothing
-        end
-    end
-end
+# function matching_terms(lchild, rchild)
+#     if lchild === rchild
+#         return (1, 1, lchild)
+#     else
+#         lterm, lconstant = find_term(lchild)
+#         rterm, rconstant = find_term(rchild)
+#         if lterm !== nothing && rterm !== nothing && lterm === rterm
+#             return (lconstant, rconstant, lterm)
+#         else
+#             return nothing
+#         end
+#     end
+# end
 
 function simplify_check_cache(::typeof(+), na, nb, cache)::Node
     a = Node(na)
@@ -262,8 +262,8 @@ function simplify_check_cache(::typeof(+), na, nb, cache)::Node
         return Node(value(a) + value(children(b)[1])) + children(b)[2]
     elseif a === b
         return 2 * a
-    elseif (tmp = matching_terms(a, b)) !== nothing
-        return (tmp[1] + tmp[2]) * tmp[3]
+        # elseif (tmp = matching_terms(a, b)) !== nothing
+        #     return (tmp[1] + tmp[2]) * tmp[3]
     else
         return check_cache((+, a, b), cache)
     end
@@ -283,8 +283,8 @@ function simplify_check_cache(::typeof(-), na, nb, cache)::Node
     elseif is_constant(a) && is_constant(b)
         return Node(value(a) - value(b))
 
-    elseif (tmp = matching_terms(a, b)) !== nothing
-        return (tmp[1] - tmp[2]) * tmp[3]
+        # elseif (tmp = matching_terms(a, b)) !== nothing
+        #     return (tmp[1] - tmp[2]) * tmp[3]
     else
         return check_cache((-, a, b), cache)
     end
diff --git a/src/Factoring.jl b/src/Factoring.jl
index 1e7bd78e..e38f2805 100644
--- a/src/Factoring.jl
+++ b/src/Factoring.jl
@@ -103,23 +103,26 @@ Base.isless(::FactorOrder, a, b) = factor_order(a, b)
 
 """returns true if a should be sorted before b"""
 function factor_order(a::FactorableSubgraph, b::FactorableSubgraph)
-    if times_used(a) > times_used(b) #num_uses of contained subgraphs always ≥ num_uses of containing subgraphs. Contained subgraphs should always be factored first. It might be that a ⊄ b, but it's still correct to factor a before b.
+
+    diffa = node_difference(a)
+    diffb = node_difference(b)
+
+
+    # if a ⊂ b then diff(a) < diff(b) where diff(x) = abs(dominating_node(a) - dominated_node(a)). Might be that a ⊄ b but it's safe to factor a first.
+    # This tests only guarantees that if a ⊂ b then a will be factored first. It could be that diff(a) < diff(b) but that a ⊄ b in which case most
+    # efficient option would be to factor whichever of a,b has highest times used. But determining subgraph containment precisely is time consuming.
+    # This ordering heuristic doesn't seem to affect efficiency of computed derivatives much but is significantly faster. 
+    if diffa < diffb
         return true
-    elseif times_used(b) > times_used(a)
+    elseif times_used(a) > times_used(b) #If a is used more times than b then factor a first. More efficient.
+        return true
+    else
         return false
-    else # if a ⊂ b then diff(a) < diff(b) where diff(x) = abs(dominating_node(a) - dominated_node(a)). Might be that a ⊄ b but it's safe to factor a first and if a ⊂ b then it will always be factored first.
-        diffa = node_difference(a)
-        diffb = node_difference(b)
-
-        if diffa < diffb
-            return true
-        else
-            return false #can factor a,b in either order 
-        end
     end
 end
 
 
+
 sort_in_factor_order!(a::AbstractVector{T}) where {T<:FactorableSubgraph} = sort!(a, lt=factor_order)
 
 
@@ -625,3 +628,32 @@ function number_of_operations(jacobian::AbstractArray{T}) where {T<:Node}
     end
     return count
 end
+
+function new_factor_subgraph!(a::FactorableSubgraph{T}) where {T}
+    local new_edge::PathEdge{T}
+    if subgraph_exists(subgraph)
+
+        if is_branching(subgraph) #handle the uncommon case of factorization creating new factorable subgraphs internal to subgraph
+            sum = evaluate_branching_subgraph(subgraph)
+            new_edge = make_factored_edge(subgraph, sum)
+        else
+            sum = evaluate_subgraph(subgraph)
+            # if value(sum) == 0
+            #     display(subgraph)
+            #     write_dot("sph.svg", graph(subgraph), value_labels=true, reachability_labels=false, start_nodes=[24])
+            # end
+
+            # # @assert value(sum) != 0
+
+            new_edge = make_factored_edge(subgraph, sum)
+        end
+        add_non_dom_edges!(subgraph)
+        #reset roots in R, if possible. All edges earlier in the path than the first vertex with more than one child cannot be reset.
+        edges_to_delete = reset_edge_masks!(subgraph)
+        for edge in edges_to_delete
+            delete_edge!(graph(subgraph), edge)
+        end
+
+        add_edge!(graph(subgraph), new_edge)
+    end
+end