diff --git a/dask_expr/tests/test_util.py b/dask_expr/tests/test_util.py
index e3ebab846..bafa54847 100644
--- a/dask_expr/tests/test_util.py
+++ b/dask_expr/tests/test_util.py
@@ -1,6 +1,43 @@
+import pickle
+
 import pytest
 
-from dask_expr._util import RaiseAttributeError
+from dask_expr._util import RaiseAttributeError, _tokenize_deterministic
+
+
+def _clear_function_cache():
+    from dask.base import function_cache, function_cache_lock
+
+    with function_cache_lock:
+        function_cache.clear()
+
+
+def tokenize(x, /, __ensure_deterministic=True, *args, **kwargs):
+    _clear_function_cache()
+    try:
+        before = _tokenize_deterministic(x, *args, **kwargs)
+        _clear_function_cache()
+        if __ensure_deterministic:
+            assert before == _tokenize_deterministic(x, *args, **kwargs)
+            _clear_function_cache()
+        try:
+            after = _tokenize_deterministic(
+                pickle.loads(pickle.dumps(x)), *args, **kwargs
+            )
+        except (AttributeError, pickle.PicklingError):
+            # If we go down this path we're almost certainly guaranteed to fail
+            # since cloudpickle dumps are not deterministic and the tokenization
+            # is relying on that
+            import cloudpickle
+
+            after = _tokenize_deterministic(
+                cloudpickle.loads(cloudpickle.dumps(x)), *args, **kwargs
+            )
+
+        assert before == after
+        return before
+    finally:
+        _clear_function_cache()
 
 
 def test_raises_attribute_error():
@@ -19,3 +56,46 @@ class B(A):
         B.x
     with pytest.raises(AttributeError, match="'B' object has no attribute 'x'"):
         B().x
+
+
+def test_tokenize_lambda():
+    func = lambda x: x + 1
+    tokenize(func)
+
+
+import pandas as pd
+
+from dask_expr import from_pandas
+
+
+def test_tokenize_deterministic():
+    ddf = from_pandas(pd.DataFrame({"a": [1, 2, 3]}))
+    assert ddf._name == ddf._name
+    tokenize(ddf._expr)
+    # This fails because there is no tokenization registered for our collection
+    # Works with https://github.com/dask/dask/pull/10808
+    # tokenize(ddf)
+
+    def identity(x):
+        return x
+
+    ddf2 = ddf.map_partitions(identity)
+    # Fails because of local functions
+
+    tokenize(ddf2._expr)
+    # tokenize(ddf2)
+
+    def identity(x):
+        return x + 1
+
+    ddf3 = ddf.map_partitions(identity)
+
+    from distributed.protocol.pickle import dumps, loads
+
+    # This works since ddf is rather trivial and tokenization for from_pandas is
+    # actually properly implemented
+    assert loads(dumps(ddf))._name == ddf._name
+
+    # This fails since the lambda is not deterministic
+    assert loads(dumps(ddf2))._name == ddf2._name
+    assert tokenize(ddf2._expr) != tokenize(ddf3._expr)