diff --git a/fe/fe-core/src/main/java/org/apache/doris/analysis/Analyzer.java b/fe/fe-core/src/main/java/org/apache/doris/analysis/Analyzer.java
index 7931705cc31d02..3737093d023f04 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/analysis/Analyzer.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/analysis/Analyzer.java
@@ -1335,6 +1335,14 @@ public void registerConjuncts(Expr e, boolean fromHavingClause) throws AnalysisE
     public void registerConjuncts(Expr e, boolean fromHavingClause, List<TupleId> ids) throws AnalysisException {
         for (Expr conjunct : e.getConjuncts()) {
             registerConjunct(conjunct);
+            if (!e.isConstant()) {
+                ArrayList<TupleId> tupleIds = Lists.newArrayList();
+                ArrayList<SlotId> slotIds = Lists.newArrayList();
+                e.getIds(tupleIds, slotIds);
+                if (tupleIds.isEmpty() && slotIds.isEmpty()) {
+                    e.setBoundTupleIds(ids);
+                }
+            }
             if (ids != null) {
                 for (TupleId id : ids) {
                     registerConstantConjunct(id, conjunct);
diff --git a/fe/fe-core/src/main/java/org/apache/doris/analysis/Expr.java b/fe/fe-core/src/main/java/org/apache/doris/analysis/Expr.java
index 6c614db71ca9d2..c087107e5e0e45 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/analysis/Expr.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/analysis/Expr.java
@@ -298,6 +298,8 @@ public boolean apply(Expr arg) {
     protected boolean printSqlInParens = false;
     protected Optional<String> exprName = Optional.empty();
 
+    protected List<TupleId> boundTupleIds = null;
+
     protected Expr() {
         super();
         type = Type.INVALID;
@@ -1293,6 +1295,9 @@ public boolean isBound(TupleId tid) {
      * Returns true if expr is fully bound by tids, otherwise false.
      */
     public boolean isBoundByTupleIds(List<TupleId> tids) {
+        if (boundTupleIds != null && !boundTupleIds.isEmpty()) {
+            return boundTupleIds.stream().anyMatch(id -> tids.contains(id));
+        }
         for (Expr child : children) {
             if (!child.isBoundByTupleIds(tids)) {
                 return false;
@@ -1301,6 +1306,10 @@ public boolean isBoundByTupleIds(List<TupleId> tids) {
         return true;
     }
 
+    public void setBoundTupleIds(List<TupleId> tids) {
+        boundTupleIds = tids;
+    }
+
 
     /**
      * Returns true if expr have child bound by tids, otherwise false.
diff --git a/regression-test/suites/correctness_p0/test_rand_filter.groovy b/regression-test/suites/correctness_p0/test_rand_filter.groovy
new file mode 100644
index 00000000000000..ccad3161caf2ce
--- /dev/null
+++ b/regression-test/suites/correctness_p0/test_rand_filter.groovy
@@ -0,0 +1,36 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+suite("test_rand_filter") {
+    sql"""set enable_nereids_planner=false;"""
+    sql """ DROP TABLE IF EXISTS test_rand_filter_t """
+    sql """
+            CREATE TABLE  test_rand_filter_t (
+                a int
+            )
+            DUPLICATE KEY(a)
+            DISTRIBUTED BY HASH(a) BUCKETS 1
+            PROPERTIES (
+              "replication_num" = "1"
+            )
+        """
+    explain {
+        sql("""select * from test_rand_filter_t where rand() < 0.5 union all select * from test_rand_filter_t where rand() > 0.3;""")
+        notContains("AND")
+    }
+    sql """ DROP TABLE IF EXISTS test_rand_filter_t """
+}