diff --git a/ax/utils/common/equality.py b/ax/utils/common/equality.py
index 1f2868f7e5b..2a0841f68e3 100644
--- a/ax/utils/common/equality.py
+++ b/ax/utils/common/equality.py
@@ -42,30 +42,45 @@ def same_elements(list1: List[Any], list2: List[Any]) -> bool:
         -- The lists do not contain duplicates
 
     Checking equality is then the same as checking that the lists are the same
-    length, and that one is a subset of the other.
+    length, and that both are subsets of the other.
     """
 
     if len(list1) != len(list2):
         return False
 
+    matched = [False] * len(list2)
     for item1 in list1:
-        found = False
-        for item2 in list2:
-            if isinstance(item1, np.ndarray) or isinstance(item2, np.ndarray):
-                if (
-                    isinstance(item1, np.ndarray)
-                    and isinstance(item2, np.ndarray)
-                    and np.array_equal(item1, item2)
-                ):
-                    found = True
-                    break
-            elif item1 == item2:
-                found = True
+        for i, item2 in enumerate(list2):
+            if not matched[i] and is_ax_equal(item1, item2):
+                matched[i] = True
                 break
-        if not found:
+        else:
             return False
+    return all(matched)
+
 
-    return True
+# pyre-fixme[2]: Parameter annotation cannot contain `Any`.
+def is_ax_equal(one_val: Any, other_val: Any) -> bool:
+    """Check for equality of two values, handling lists, dicts, dfs, floats,
+    dates, and numpy arrays.  This method and ``same_elements`` function
+    as a recursive unit.
+    """
+    if isinstance(one_val, list) and isinstance(other_val, list):
+        return same_elements(one_val, other_val)
+    elif isinstance(one_val, dict) and isinstance(other_val, dict):
+        return sorted(one_val.keys()) == sorted(other_val.keys()) and same_elements(
+            list(one_val.values()), list(other_val.values())
+        )
+    elif isinstance(one_val, np.ndarray) and isinstance(other_val, np.ndarray):
+        return np.array_equal(one_val, other_val, equal_nan=True)
+    elif isinstance(one_val, datetime):
+        return datetime_equals(one_val, other_val)
+    elif isinstance(one_val, float) and isinstance(other_val, float):
+        return np.isclose(one_val, other_val, equal_nan=True)
+    elif isinstance(one_val, pd.DataFrame) and isinstance(other_val, pd.DataFrame):
+        return dataframe_equals(one_val, other_val)
+    else:
+        return one_val == other_val
 
 
 def datetime_equals(dt1: Optional[datetime], dt2: Optional[datetime]) -> bool:
@@ -198,25 +213,8 @@ def object_attribute_dicts_find_unequal_fields(
                     and isinstance(one_val.model, type(other_val.model))
                 )
 
-        elif isinstance(one_val, list):
-            equal = isinstance(other_val, list) and same_elements(one_val, other_val)
-        elif isinstance(one_val, dict):
-            equal = isinstance(other_val, dict) and sorted(one_val.keys()) == sorted(
-                other_val.keys()
-            )
-            equal = equal and same_elements(
-                list(one_val.values()), list(other_val.values())
-            )
-        elif isinstance(one_val, np.ndarray):
-            equal = np.array_equal(one_val, other_val, equal_nan=True)
-        elif isinstance(one_val, datetime):
-            equal = datetime_equals(one_val, other_val)
-        elif isinstance(one_val, float):
-            equal = np.isclose(one_val, other_val)
-        elif isinstance(one_val, pd.DataFrame):
-            equal = dataframe_equals(one_val, other_val)
         else:
-            equal = one_val == other_val
+            equal = is_ax_equal(one_val, other_val)
 
         if not equal:
             unequal_value[field] = (one_val, other_val)
diff --git a/ax/utils/common/tests/test_equality.py b/ax/utils/common/tests/test_equality.py
index 4d2df2fc509..e21e49dd966 100644
--- a/ax/utils/common/tests/test_equality.py
+++ b/ax/utils/common/tests/test_equality.py
@@ -34,8 +34,15 @@ def eq(x, y):
     def test_ListsEquals(self) -> None:
         self.assertFalse(same_elements([0], [0, 1]))
         self.assertFalse(same_elements([1, 0], [0, 2]))
+        self.assertFalse(same_elements([1, 1], [1, 2]))
+        self.assertFalse(same_elements([1, 2], [1, 1]))
+        self.assertFalse(same_elements([1, 1, 2], [1, 2, 2]))
         self.assertTrue(same_elements([1, 0], [0, 1]))
 
+    def test_ListsEquals_floats(self) -> None:
+        self.assertTrue(same_elements([0.0], [0.000000000000001]))
+        self.assertTrue(same_elements([float("nan")], [float("nan")]))
+
     def test_DatetimeEquals(self) -> None:
         now = datetime.now()
         self.assertTrue(datetime_equals(None, None))