diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/FilterEstimation.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/FilterEstimation.java
index 9c04b59ce6df6b..d5c9ded22e360d 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/FilterEstimation.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/FilterEstimation.java
@@ -512,6 +512,10 @@ private Statistics estimateColumnLessThanColumn(Expression leftExpr, ColumnStati
             context.addKeyIfSlot(rightExpr);
             return statistics;
         }
+        if (leftRange.isInfinite() || rightRange.isInfinite()) {
+            return context.statistics.withSel(DEFAULT_INEQUALITY_COEFFICIENT);
+        }
+
         double leftOverlapPercent = leftRange.overlapPercentWith(rightRange);
         // Left always greater than right
         if (leftOverlapPercent == 0) {
diff --git a/fe/fe-core/src/main/java/org/apache/doris/statistics/StatisticRange.java b/fe/fe-core/src/main/java/org/apache/doris/statistics/StatisticRange.java
index 74b77c2ee7c91f..7b7b08ab24669d 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/statistics/StatisticRange.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/statistics/StatisticRange.java
@@ -239,4 +239,8 @@ public double getDistinctValues() {
         return distinctValues;
     }
 
+    @Override
+    public String toString() {
+        return "(" + lowExpr + "," + highExpr + ")";
+    }
 }