diff --git a/pymbolic/mapper/__init__.py b/pymbolic/mapper/__init__.py
index c549938d13b62438593b153b34b9fa838b0b385a..e4f1dc1f800f4fcde3ffc6749b4d3dc3e914f596 100644
--- a/pymbolic/mapper/__init__.py
+++ b/pymbolic/mapper/__init__.py
@@ -210,3 +210,21 @@ class IdentityMapper(IdentityMapperBase, RecursiveMapper):
 
 class NonrecursiveIdentityMapper(IdentityMapperBase, Mapper):
     pass
+
+
+
+
+class CSECachingMapperMixin(object):
+    def map_common_subexpression(self, expr):
+        try:
+            ccd = self._cse_cache_dict
+        except AttributeError:
+            from weakref import WeakKeyDictionary
+            ccd = self._cse_cache_dict = WeakKeyDictionary()
+
+        try:
+            return ccd[expr]
+        except KeyError:
+            result = self.map_common_subexpression_uncached(expr)
+            ccd[expr] = result
+            return result
diff --git a/pymbolic/mapper/constant_folder.py b/pymbolic/mapper/constant_folder.py
index 680375f59a69ac1f69e0430a5c6d86283492d3a5..8e6cf0704859c7a34a673046cab8a4c4af873f3e 100644
--- a/pymbolic/mapper/constant_folder.py
+++ b/pymbolic/mapper/constant_folder.py
@@ -1,4 +1,7 @@
-from pymbolic.mapper import IdentityMapper, NonrecursiveIdentityMapper
+from pymbolic.mapper import \
+        IdentityMapper, \
+        NonrecursiveIdentityMapper, \
+        CSECachingMapperMixin
 
 
 
@@ -61,20 +64,35 @@ class CommutativeConstantFoldingMapperBase(ConstantFoldingMapperBase):
 
 
 
-class ConstantFoldingMapper(ConstantFoldingMapperBase, IdentityMapper):
-    pass
+class ConstantFoldingMapper(
+        CSECachingMapperMixin, 
+        ConstantFoldingMapperBase, 
+        IdentityMapper):
+
+    map_common_subexpression_uncached = \
+            IdentityMapper.map_common_subexpression
 
 class NonrecursiveConstantFoldingMapper(
+        CSECachingMapperMixin,
         NonrecursiveIdentityMapper, 
         ConstantFoldingMapperBase):
-    pass
 
-class CommutativeConstantFoldingMapper(CommutativeConstantFoldingMapperBase,
+    map_common_subexpression_uncached = \
+            NonrecursiveIdentityMapper.map_common_subexpression
+
+class CommutativeConstantFoldingMapper(
+        CSECachingMapperMixin,
+        CommutativeConstantFoldingMapperBase,
         IdentityMapper):
-    pass
+
+    map_common_subexpression_uncached = \
+            IdentityMapper.map_common_subexpression
 
 class NonrecursiveCommutativeConstantFoldingMapper(
+        CSECachingMapperMixin,
         CommutativeConstantFoldingMapperBase,
         NonrecursiveIdentityMapper,):
-    pass
+
+    map_common_subexpression_uncached = \
+            NonrecursiveIdentityMapper.map_common_subexpression
 
diff --git a/pymbolic/mapper/dependency.py b/pymbolic/mapper/dependency.py
index e299c004848dd7234ef01d95b6387fa05472ccf0..832cf53c68c2d19dbe6922900784020bf943f6e1 100644
--- a/pymbolic/mapper/dependency.py
+++ b/pymbolic/mapper/dependency.py
@@ -1,9 +1,9 @@
-from pymbolic.mapper import CombineMapper
+from pymbolic.mapper import CombineMapper, CSECachingMapperMixin
 
 
 
 
-class DependencyMapper(CombineMapper):
+class DependencyMapper(CSECachingMapperMixin, CombineMapper):
     def __init__(self, 
             include_subscripts=True, 
             include_lookups=True,
@@ -62,7 +62,7 @@ class DependencyMapper(CombineMapper):
         else:
             return CombineMapper.map_subscript(self, expr)
 
-    def map_common_subexpression(self, expr):
+    def map_common_subexpression_uncached(self, expr):
         if self.include_cses:
             return set([expr])
         else:
diff --git a/pymbolic/primitives.py b/pymbolic/primitives.py
index 7a654f1d482aeaa2edb9cc07df14c2837897de48..64bd06f1dc2a6bcd3fb1e94b2f55ab34900ce7e7 100644
--- a/pymbolic/primitives.py
+++ b/pymbolic/primitives.py
@@ -156,7 +156,7 @@ class Expression(object):
         Subclasses should generally not override this method, but instead 
         provide an implementation of L{is_equal}.
         """
-        if id(self) == id(other):
+        if self is other:
             return True
         elif hash(self) != hash(other):
             return False