diff --git a/dask_expr/_core.py b/dask_expr/_core.py
index afff3be16..afedefb8a 100644
--- a/dask_expr/_core.py
+++ b/dask_expr/_core.py
@@ -48,6 +48,7 @@ def __new__(cls, *args, **kwargs):
             return Expr._instances[_name]
 
         Expr._instances[_name] = inst
+        inst.simplified = False
         if inst._required_attribute:
             dep = next(iter(_dependencies))._meta
             if not hasattr(dep, inst._required_attribute):
@@ -299,9 +300,12 @@ def simplify_once(self, dependents: defaultdict):
         expr:
             output expression
         """
+        if self.simplified:
+            return self
         expr = self
-
+        n = 0
         while True:
+            n += 1
             out = expr._simplify_down()
             if out is None:
                 out = expr
@@ -338,7 +342,7 @@ def simplify_once(self, dependents: defaultdict):
                 expr = type(expr)(*new_operands)
 
             break
-
+        expr.simplified = True
         return expr
 
     def simplify(self) -> Expr:
@@ -349,6 +353,7 @@ def simplify(self) -> Expr:
             if new._name == expr._name:
                 break
             expr = new
+        # print(f"Cache has size {len(_seen)=}")
         return expr
 
     def _simplify_down(self):