diff --git a/fe/fe-core/src/test/java/org/apache/doris/nereids/trees/expressions/functions/scalar/UniqueFunctionTest.java b/fe/fe-core/src/test/java/org/apache/doris/nereids/trees/expressions/functions/scalar/UniqueFunctionTest.java
index e0a6986492c07a..0f16a266f491a2 100644
--- a/fe/fe-core/src/test/java/org/apache/doris/nereids/trees/expressions/functions/scalar/UniqueFunctionTest.java
+++ b/fe/fe-core/src/test/java/org/apache/doris/nereids/trees/expressions/functions/scalar/UniqueFunctionTest.java
@@ -169,7 +169,8 @@ void testNoAggregate2() {
         Map<ExprId, Expression> exprIdToOriginExprMap = getExprIdToOriginExpressionMap(root);
 
         LogicalProject<?> project = (LogicalProject<?>) root.child(0);
-        Assertions.assertEquals(ImmutableList.of("a + random()", "a + random()",
+        Assertions.assertEquals(ImmutableList.of("(a + random()) AS `a + random()`",
+                        "(a + random()) AS `a + random()`",
                         "sum(a + random()) over(partition by a + random())", "sum(a + random()) over(partition by a + random())"),
                 toSqls(project.getProjects()));
         checkOutputDifferent(project, expressionSet, exprIdToOriginExprMap);
@@ -811,7 +812,8 @@ void testAggregateWithGroupBy5() {
 
         LogicalProject<?> project = (LogicalProject<?>) root.child(0);
         Assertions.assertEquals(ImmutableList.of("a + random()", "a + random() + 1", "a + random() + 2",
-                        "sum(a + random())", "sum(a + random() + 1)", "sum(a + random() + 2)",
+                        "sum(a + random()) AS `sum(a + random())`", "sum(a + random() + 1) AS `sum(a + random() + 1)`",
+                        "sum((a + random() + cast(2 as DOUBLE))) AS `sum(a + random() + 2)`",
                         "sum(a + random()) over()", "sum(a + random() + 1) over()", "sum(a + random() + 2) over()"),
                 toSqls(project.getProjects()));
         Lists.transform(ImmutableList.of(0, 2, 3, 5, 6, 8), project.getProjects()::get).forEach(random0EqualValidator::checkRandomEqual);
diff --git a/regression-test/data/nereids_rules_p0/unique_function/agg_with_unique_function.out b/regression-test/data/nereids_rules_p0/unique_function/agg_with_unique_function.out
index 00ea2481b25fd0..a59eb1d160d45e 100644
--- a/regression-test/data/nereids_rules_p0/unique_function/agg_with_unique_function.out
+++ b/regression-test/data/nereids_rules_p0/unique_function/agg_with_unique_function.out
@@ -16,38 +16,38 @@ PhysicalResultSink
 
 -- !check_equal_no_agg_4_shape --
 PhysicalResultSink
---PhysicalProject[a + random(), a + random(), sum(a + random()) over() AS `sum(a + random()) over()`, sum(a + random()) over() AS `sum(a + random()) over()`]
+--PhysicalProject[(a + random()) AS `a + random()`, (a + random()) AS `a + random()`, sum(a + random()) over() AS `sum(a + random()) over()`, sum(a + random()) over() AS `sum(a + random()) over()`]
 ----PhysicalWindow
-------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `a + random()`, (a + random()) AS `a + random()`]
+------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, tbl_unique_function_with_one_row.a]
 --------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_no_agg_5_shape --
 PhysicalResultSink
---PhysicalProject[a + random(), a + random()]
+--PhysicalProject[(a + random()) AS `a + random()`, (a + random()) AS `a + random()`]
 ----filter((sum((a + random())) OVER() > 0.01) and (sum((a + random())) OVER(PARTITION BY (a + random())) > 0.01))
 ------PhysicalWindow
 --------PhysicalWindow
 ----------PhysicalQuickSort[LOCAL_SORT]
-------------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `a + random()`, (a + random()) AS `a + random()`]
+------------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, tbl_unique_function_with_one_row.a]
 --------------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_no_agg_6_shape --
 PhysicalResultSink
---PhysicalProject[a + random(), a + random(), sum(a + random()) over (partition by a + random())]
+--PhysicalProject[(a + random()) AS `a + random()`, (a + random()) AS `a + random()`, sum(a + random()) over (partition by a + random())]
 ----filter((sum((a + random())) OVER() > 0.01) and (sum((a + random())) OVER(PARTITION BY (a + random())) > 0.01))
 ------PhysicalWindow
 --------PhysicalWindow
 ----------PhysicalQuickSort[LOCAL_SORT]
 ------------PhysicalWindow
 --------------PhysicalQuickSort[LOCAL_SORT]
-----------------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `a + random()`, (a + random()) AS `a + random()`]
+----------------PhysicalProject[(a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, (a + random()) AS `(a + random())`, tbl_unique_function_with_one_row.a]
 ------------------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_one_row_to_agg_1_shape --
 PhysicalResultSink
---PhysicalProject[random(), random(), sum(random()), sum(random()), sum(random()) over() AS `sum(random()) over()`, sum(random()) over() AS `sum(random()) over()`]
+--PhysicalProject[random() AS `random()`, random() AS `random()`, sum(random()), sum(random()), sum(random()) over() AS `sum(random()) over()`, sum(random()) over() AS `sum(random()) over()`]
 ----PhysicalWindow
-------PhysicalProject[random() AS `random()`, random() AS `random()`, random() AS `random()`, random() AS `random()`, sum(random()), sum(random())]
+------PhysicalProject[random() AS `random()`, random() AS `random()`, sum(random()), sum(random())]
 --------hashAgg[GLOBAL]
 ----------hashAgg[LOCAL]
 ------------PhysicalProject[random() AS `random()`, random() AS `random()`]
@@ -168,37 +168,34 @@ PhysicalResultSink
 
 -- !check_equal_agg_with_groupby_7_shape --
 PhysicalResultSink
---PhysicalProject[a + random(), a + random() AS `a + random()`, sum(a + random()), sum(a + random()) over() AS `sum(a + random()) over()`]
+--PhysicalProject[a + random(), a + random() AS `a + random()`, sum(a + random()) AS `sum(a + random())`, sum(a + random()) over() AS `sum(a + random()) over()`]
 ----PhysicalWindow
-------PhysicalProject[a + random() AS `a + random()`, sum(a + random()) AS `sum(a + random())`]
---------hashAgg[GLOBAL]
-----------hashAgg[LOCAL]
-------------PhysicalProject[(a + random()) AS `a + random()`]
---------------PhysicalOlapScan[tbl_unique_function_with_one_row]
+------hashAgg[GLOBAL]
+--------hashAgg[LOCAL]
+----------PhysicalProject[(a + random()) AS `a + random()`]
+------------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_agg_with_groupby_8_shape --
 PhysicalResultSink
---PhysicalProject[a + random(), a + random() AS `a + random()`, sum(a + random()), sum(a + random()) over() AS `sum(a + random()) over()`]
+--PhysicalProject[a + random(), a + random() AS `a + random()`, sum(a + random()) AS `sum(a + random())`, sum(a + random()) over() AS `sum(a + random()) over()`]
 ----PhysicalWindow
-------PhysicalProject[a + random() AS `a + random()`, sum(a + random()) AS `sum(a + random())`]
---------hashAgg[GLOBAL]
-----------hashAgg[LOCAL]
-------------filter((a + random() > 0.01))
---------------PhysicalProject[(a + random()) AS `a + random()`]
-----------------PhysicalOlapScan[tbl_unique_function_with_one_row]
+------hashAgg[GLOBAL]
+--------hashAgg[LOCAL]
+----------filter((a + random() > 0.01))
+------------PhysicalProject[(a + random()) AS `a + random()`]
+--------------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_agg_with_groupby_9_shape --
 PhysicalResultSink
 --PhysicalQuickSort[MERGE_SORT]
 ----PhysicalQuickSort[LOCAL_SORT]
-------PhysicalProject[a + random(), a + random() AS `a + random()`, abs(a + random()), sum(a + random()), sum(a + random()) over() AS `sum(a + random()) over()`]
+------PhysicalProject[a + random(), a + random() AS `a + random()`, abs(a + random()) AS `abs(a + random())`, sum(a + random()) AS `sum(a + random())`, sum(a + random()) over() AS `sum(a + random()) over()`]
 --------PhysicalWindow
-----------PhysicalProject[a + random() AS `a + random()`, abs(a + random()) AS `abs(a + random())`, sum(a + random()) AS `sum(a + random())`]
-------------hashAgg[GLOBAL]
---------------hashAgg[LOCAL]
-----------------filter((a + random() > 0.01))
-------------------PhysicalProject[(a + random()) AS `a + random()`]
---------------------PhysicalOlapScan[tbl_unique_function_with_one_row]
+----------hashAgg[GLOBAL]
+------------hashAgg[LOCAL]
+--------------filter((a + random() > 0.01))
+----------------PhysicalProject[(a + random()) AS `a + random()`]
+------------------PhysicalOlapScan[tbl_unique_function_with_one_row]
 
 -- !check_equal_agg_with_groupby_10_shape --
 PhysicalResultSink