diff --git a/Graphiti/Core/ExprLow.lean b/Graphiti/Core/ExprLow.lean
index b8bb32d..12d9592 100644
--- a/Graphiti/Core/ExprLow.lean
+++ b/Graphiti/Core/ExprLow.lean
@@ -518,19 +518,100 @@ def comm_connection_inv (e : ExprLow Ident Typ) := fix_point_opt comm_connection
 
 def comm_base (binst : PortMapping Ident) (btyp : Typ) e := fix_point_opt (comm_base_ binst btyp) e 10000
 
-def comm_connections' {Ident} [DecidableEq Ident] (conn : List (Connection Ident)) (e : ExprLow Ident Typ): ExprLow Ident Typ :=
-  conn.foldr comm_connection' e
-
 def comm_connections {Ident} [DecidableEq Ident] (conn : List (Connection Ident)) (e : ExprLow Ident Typ): ExprLow Ident Typ :=
   conn.foldr comm_connection e
 
-def comm_bases {Ident} [DecidableEq Ident] (bases : List (PortMapping Ident × Typ)) (e : ExprLow Ident Typ): ExprLow Ident Typ :=
-  bases.foldr (Function.uncurry ExprLow.comm_base) e
-
 def getPortMaps {α β} : ExprLow α β → List (PortMapping α)
 | .base inst typ => [inst]
 | .connect c e => getPortMaps e
 | .product e₁ e₂ => getPortMaps e₁ ++ getPortMaps e₂
 
+def comm_base_only_conn {Ident Typ} [DecidableEq Ident] [DecidableEq Typ]
+  (binst : PortMapping Ident) (btyp : Typ) (e : ExprLow Ident Typ) : Nat → ExprLow Ident Typ
+| 0 => e
+| n+1 =>
+  match e with
+  | .product e₁ e₂ =>
+    if e₁ = .base binst btyp then
+      match e₂ with
+      | .connect c e =>
+        if c.output ∉ binst.output.valsList ∧ c.input ∉ binst.input.valsList then
+          .connect c <| (comm_base_only_conn binst btyp (.product e₁ e) n)
+        else .product e₁ e₂
+      | _ => .product e₁ e₂
+    else .product e₁ <| comm_base_only_conn binst btyp e₂ n
+  | .connect c e => .connect c <| comm_base_only_conn binst btyp e n
+  | e => e
+
+def comm_bases_only_conn {Ident Typ} [DecidableEq Ident] [DecidableEq Typ]
+    (bases : List (PortMapping Ident × Typ)) (e : ExprLow Ident Typ) : ExprLow Ident Typ :=
+  bases.foldr (Function.uncurry (fun a b c => ExprLow.comm_base_only_conn a b c 10000000)) e
+
+def comm_base_fast {Ident Typ} [DecidableEq Ident] [DecidableEq Typ]
+  (binst : PortMapping Ident) (btyp : Typ) (e : ExprLow Ident Typ) : Nat → ExprLow Ident Typ
+| 0 => e
+| n+1 =>
+  match e with
+  | .product e₁ e₂ =>
+    if e₁ = .base binst btyp then
+      match e₂ with
+      | .connect c e =>
+        if c.output ∉ binst.output.valsList ∧ c.input ∉ binst.input.valsList then
+          .connect c <| (comm_base_fast binst btyp (.product e₁ e) n)
+        else .product e₁ e₂
+      | .product (.base binst' btyp') e₂' =>
+        if inst_disjoint binst' binst then
+          .product (.base binst' btyp') (comm_base_fast binst btyp (.product e₁ e₂') n)
+        else .product e₁ e₂
+      | .base binst' btyp' =>
+        if inst_disjoint binst' binst then .product e₂ e₁ else .product e₁ e₂
+      | _ => .product e₁ e₂
+    else .product e₁ <| comm_base_fast binst btyp e₂ n
+  | .connect c e => .connect c <| comm_base_fast binst btyp e n
+  | e => e
+
+def comm_bases_fast
+    (bases : List (PortMapping Ident × Typ)) (e : ExprLow Ident Typ) : ExprLow Ident Typ :=
+  bases.foldr (Function.uncurry (fun a b c => ExprLow.comm_base_fast a b c 10000000)) e
+
+def comm_connection'_fast (conn : Connection Ident) (e_strt : ExprLow Ident Typ) : Nat → ExprLow Ident Typ
+| 0 => e_strt
+| n+1 =>
+  match e_strt with
+  | .connect c e =>
+    if c.output = conn.output ∧ c.input = conn.input then
+      match e with
+      | .connect c' e' =>
+        if c.output ≠ c'.output ∧ c.input ≠ c'.input then
+          .connect c' (comm_connection'_fast conn (.connect c e') n)
+        else e_strt
+      | .product e₁ e₂ =>
+        let a := e₁.findInput c.input
+        let b := e₁.findOutput c.output
+        if a ∧ b then
+          -- .product (comm_connection' conn <| .connect o i e₁) e₂
+          -- We actually don't want to commute (assuming we are left associative)
+          e_strt
+        else if ¬ a ∧ ¬ b ∧ e₂.findInput c.input ∧ e₂.findOutput c.output then
+          .product e₁ (comm_connection'_fast conn (.connect c e₂) n)
+        else e_strt
+      | _ => e_strt
+    else .connect c (comm_connection'_fast conn e n)
+  | .product e₁ e₂ =>
+    .product (comm_connection'_fast conn e₁ n) (comm_connection'_fast conn e₂ n)
+  | e => e
+
+def comm_connections'_fast
+    (conn : List (Connection Ident)) (e : ExprLow Ident Typ) : ExprLow Ident Typ :=
+  conn.foldr (fun a b => ExprLow.comm_connection'_fast a b 10000000) e
+
+@[implemented_by comm_connections'_fast]
+def comm_connections' (conn : List (Connection Ident)) (e : ExprLow Ident Typ): ExprLow Ident Typ :=
+  conn.foldr comm_connection' e
+
+@[implemented_by comm_bases_fast]
+def comm_bases (bases : List (PortMapping Ident × Typ)) (e : ExprLow Ident Typ): ExprLow Ident Typ :=
+  bases.foldr (Function.uncurry ExprLow.comm_base) e
+
 end ExprLow
 end Graphiti