diff --git a/ufl/coefficient.py b/ufl/coefficient.py
index c10eeb1de..90d20316c 100644
--- a/ufl/coefficient.py
+++ b/ufl/coefficient.py
@@ -205,6 +205,7 @@ def __repr__(self):
         return self._repr
 
     @Expr.traverse_dag
+    @Expr.traverse_dag_apply_coefficient_split_cache
     def traverse_dag_apply_coefficient_split(
         self,
         coefficient_split,
@@ -214,6 +215,7 @@ def traverse_dag_apply_coefficient_split(
         cache=None,
     ):
         from ufl.classes import (
+            Terminal,
             ComponentTensor,
             MultiIndex,
             NegativeRestricted,
@@ -228,25 +230,14 @@ def traverse_dag_apply_coefficient_split(
         from ufl.tensors import as_tensor
 
         if self not in coefficient_split:
-            c = self
-            if reference_value:
-                c = ReferenceValue(c)
-            for _ in range(reference_grad):
-                # Return zero if expression is trivially constant. This has to
-                # happen here because ReferenceGrad has no access to the
-                # topological dimension of a literal zero.
-                if is_cellwise_constant(c):
-                    dim = extract_unique_domain(subcoeff).topological_dimension()
-                    c = Zero(c.ufl_shape + (dim,), c.ufl_free_indices, c.ufl_index_dimensions)
-                else:
-                    c = ReferenceGrad(c)
-            if restricted == "+":
-                c = PositiveRestricted(c)
-            elif restricted == "-":
-                c = NegativeRestricted(c)
-            elif restricted is not None:
-                raise RuntimeError(f"Got unknown restriction: {restricted}")
-            return c
+            return Terminal.traverse_dag_apply_coefficient_split(
+                self,
+                coefficient_split,
+                reference_value=reference_value,
+                reference_grad=reference_grad,
+                restricted=restricted,
+                cache=cache,
+            )
         # Reference value expected
         if not reference_value:
             raise RuntimeError(f"ReferenceValue expected: got {o}")
diff --git a/ufl/core/expr.py b/ufl/core/expr.py
index 2179d4821..fa93e18ec 100644
--- a/ufl/core/expr.py
+++ b/ufl/core/expr.py
@@ -430,6 +430,39 @@ def traverse_dag_reuse_if_untouched(self, method_name: str, *args, **kwargs) ->
         else:
             return self._ufl_expr_reconstruct_(*ops)
 
+    @staticmethod
+    def traverse_dag_apply_coefficient_split_cache(f):
+        """Use method specific key for caching."""
+        @functools.wraps(f)
+        def wrapper(
+            self,
+            coefficient_split,
+            reference_value=False,
+            reference_grad=0,
+            restricted=None,
+            cache=None,
+        ):
+            if cache is None:
+                raise RuntimeError(f"""
+                    Can not have cache=None.
+                    Must decorate {f} with ``Expr.traverse_dag``.
+                """)
+            key = (self, reference_value, reference_grad, restricted)
+            if key in cache:
+                return cache[key]
+            else:
+                result = f(
+                    self,
+                    coefficient_split,
+                    reference_value=reference_value,
+                    reference_grad=reference_grad,
+                    restricted=restricted,
+                    cache=cache,
+                )
+                cache[key] = result
+                return result
+        return wrapper
+
     def __getattr__(self, name):
         if name.startswith(PREFIX_TRAVERSE_DAG):
             # Traverse DAG with reuse_if_untouched by default.
diff --git a/ufl/core/terminal.py b/ufl/core/terminal.py
index 9ec56bc5a..918d3aab3 100644
--- a/ufl/core/terminal.py
+++ b/ufl/core/terminal.py
@@ -93,6 +93,8 @@ def __eq__(self, other):
         """Default comparison of terminals just compare repr strings."""
         return repr(self) == repr(other)
 
+    @Expr.traverse_dag
+    @Expr.traverse_dag_apply_coefficient_split_cache
     def traverse_dag_apply_coefficient_split(
         self,
         coefficient_split,
diff --git a/ufl/differentiation.py b/ufl/differentiation.py
index 07392de89..59d7a7788 100644
--- a/ufl/differentiation.py
+++ b/ufl/differentiation.py
@@ -345,6 +345,7 @@ def __str__(self):
         return "reference_grad(%s)" % self.ufl_operands[0]
 
     @Expr.traverse_dag
+    @Expr.traverse_dag_apply_coefficient_split_cache
     def traverse_dag_apply_coefficient_split(
         self,
         coefficient_split,
diff --git a/ufl/referencevalue.py b/ufl/referencevalue.py
index 9af39dcf7..0f0c53417 100644
--- a/ufl/referencevalue.py
+++ b/ufl/referencevalue.py
@@ -37,6 +37,7 @@ def __str__(self):
         return f"reference_value({self.ufl_operands[0]})"
 
     @Expr.traverse_dag
+    @Expr.traverse_dag_apply_coefficient_split_cache
     def traverse_dag_apply_coefficient_split(
         self,
         coefficient_split: dict,
diff --git a/ufl/restriction.py b/ufl/restriction.py
index 7ac098b0b..1a27f4d96 100644
--- a/ufl/restriction.py
+++ b/ufl/restriction.py
@@ -50,6 +50,7 @@ def __str__(self):
         return f"{parstr(self.ufl_operands[0], self)}({self._side})"
 
     @Expr.traverse_dag
+    @Expr.traverse_dag_apply_coefficient_split_cache
     def traverse_dag_apply_coefficient_split(
         self,
         coefficient_split,