diff --git a/pymbolic/mapper/__init__.py b/pymbolic/mapper/__init__.py
index 5303c789631506c7cc0ff57b60d894742e737028..2536de17f2565b8dd0f32f2236314364a0b7fd35 100644
--- a/pymbolic/mapper/__init__.py
+++ b/pymbolic/mapper/__init__.py
@@ -231,7 +231,10 @@ class CachedMapper(Mapper):
             *self* does not store any mutable state. Derived mappers must
             override this method.
         """
-        return (expr, args, tuple(sorted(kwargs.items())))
+        # Must add 'type(expr)', to differentiate between python scalar types.
+        # In Python, the following conditions are true: "hash(4) == hash(4.0)"
+        # and "4 == 4.0", but their traversal results cannot be re-used.
+        return (type(expr), expr, args, tuple(sorted(kwargs.items())))
 
     def __call__(self, expr, *args, **kwargs):
         cache_key = self.get_cache_key(expr, *args, **kwargs)
diff --git a/test/test_pymbolic.py b/test/test_pymbolic.py
index 18e6cefc2c07ef8bfe614076be5f5728e101f98b..08a9d81cd24fe52dbc147ec561d2ca4e952e7510 100644
--- a/test/test_pymbolic.py
+++ b/test/test_pymbolic.py
@@ -925,6 +925,16 @@ def test_cached_mapper_memoizes():
 
         # }}}
 
+
+def test_cached_mapper_differentiates_float_int():
+    # pymbolic.git<=d343cf14 failed this regression.
+    from pymbolic.mapper import CachedIdentityMapper
+    expr = prim.Sum((4, 4.0))
+    cached_mapper = CachedIdentityMapper()
+    new_expr = cached_mapper(expr)
+    assert isinstance(new_expr.children[0], int)
+    assert isinstance(new_expr.children[1], float)
+
 # }}}