diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/ExpressionEstimation.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/ExpressionEstimation.java
index 126e90417213125..f76f63218ca0d8c 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/ExpressionEstimation.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/stats/ExpressionEstimation.java
@@ -41,6 +41,7 @@
 import org.apache.doris.nereids.trees.expressions.VirtualSlotReference;
 import org.apache.doris.nereids.trees.expressions.WhenClause;
 import org.apache.doris.nereids.trees.expressions.functions.BoundFunction;
+import org.apache.doris.nereids.trees.expressions.functions.agg.AggregateFunction;
 import org.apache.doris.nereids.trees.expressions.functions.agg.Avg;
 import org.apache.doris.nereids.trees.expressions.functions.agg.Count;
 import org.apache.doris.nereids.trees.expressions.functions.agg.Max;
@@ -128,6 +129,10 @@ public static ColumnStatistic estimate(Expression expression, Statistics stats)
 
     @Override
     public ColumnStatistic visit(Expression expr, Statistics context) {
+        ColumnStatistic stats = context.findColumnStatistics(expr);
+        if (stats != null) {
+            return stats;
+        }
         List<Expression> childrenExpr = expr.children();
         if (CollectionUtils.isEmpty(childrenExpr)) {
             return ColumnStatistic.UNKNOWN;
@@ -135,26 +140,28 @@ public ColumnStatistic visit(Expression expr, Statistics context) {
         return expr.child(0).accept(this, context);
     }
 
-    //TODO: case-when need to re-implemented
     @Override
     public ColumnStatistic visitCaseWhen(CaseWhen caseWhen, Statistics context) {
         double ndv = caseWhen.getWhenClauses().size();
+        double width = 1;
         if (caseWhen.getDefaultValue().isPresent()) {
             ndv += 1;
         }
         for (WhenClause clause : caseWhen.getWhenClauses()) {
             ColumnStatistic colStats = ExpressionEstimation.estimate(clause.getResult(), context);
             ndv = Math.max(ndv, colStats.ndv);
+            width = Math.max(width, clause.getResult().getDataType().width());
         }
         if (caseWhen.getDefaultValue().isPresent()) {
             ColumnStatistic colStats = ExpressionEstimation.estimate(caseWhen.getDefaultValue().get(), context);
             ndv = Math.max(ndv, colStats.ndv);
+            width = Math.max(width, caseWhen.getDefaultValue().get().getDataType().width());
         }
         return new ColumnStatisticBuilder()
                 .setNdv(ndv)
                 .setMinValue(Double.NEGATIVE_INFINITY)
                 .setMaxValue(Double.POSITIVE_INFINITY)
-                .setAvgSizeByte(8)
+                .setAvgSizeByte(width)
                 .setNumNulls(0)
                 .build();
     }
@@ -162,15 +169,20 @@ public ColumnStatistic visitCaseWhen(CaseWhen caseWhen, Statistics context) {
     @Override
     public ColumnStatistic visitIf(If ifClause, Statistics context) {
         double ndv = 2;
+        double width = 1;
         ColumnStatistic colStatsThen = ExpressionEstimation.estimate(ifClause.child(1), context);
         ndv = Math.max(ndv, colStatsThen.ndv);
+        width = Math.max(width, ifClause.child(1).getDataType().width());
+
         ColumnStatistic colStatsElse = ExpressionEstimation.estimate(ifClause.child(2), context);
         ndv = Math.max(ndv, colStatsElse.ndv);
+        width = Math.max(width, ifClause.child(2).getDataType().width());
+
         return new ColumnStatisticBuilder()
                 .setNdv(ndv)
                 .setMinValue(Double.NEGATIVE_INFINITY)
                 .setMaxValue(Double.POSITIVE_INFINITY)
-                .setAvgSizeByte(8)
+                .setAvgSizeByte(width)
                 .setNumNulls(0)
                 .build();
     }
@@ -242,9 +254,9 @@ public ColumnStatistic visitLiteral(Literal literal, Statistics context) {
         return new ColumnStatisticBuilder()
                 .setMaxValue(literalVal)
                 .setMinValue(literalVal)
-                .setNdv(1)
+                .setNdv(literal.isNullLiteral() ? 0 : 1)
                 .setNumNulls(literal.isNullLiteral() ? 1 : 0)
-                .setAvgSizeByte(1)
+                .setAvgSizeByte(literal.getWidth())
                 .setMinExpr(literal.toLegacyLiteral())
                 .setMaxExpr(literal.toLegacyLiteral())
                 .build();
@@ -343,8 +355,7 @@ public ColumnStatistic visitMin(Min min, Statistics context) {
             return ColumnStatistic.UNKNOWN;
         }
         // if this is scalar agg, we will update count and ndv to 1 when visiting group clause
-        return new ColumnStatisticBuilder(columnStat)
-                .build();
+        return new ColumnStatisticBuilder(columnStat).build();
     }
 
     @Override
@@ -355,15 +366,21 @@ public ColumnStatistic visitMax(Max max, Statistics context) {
             return ColumnStatistic.UNKNOWN;
         }
         // if this is scalar agg, we will update count and ndv to 1 when visiting group clause
-        return new ColumnStatisticBuilder(columnStat)
-                .build();
+        return new ColumnStatisticBuilder(columnStat).build();
     }
 
     @Override
     public ColumnStatistic visitCount(Count count, Statistics context) {
         double width = count.getDataType().width();
         // for scalar agg, ndv and row count will be normalized by 1 in StatsCalculator.computeAggregate()
+<<<<<<< HEAD
         return new ColumnStatisticBuilder(ColumnStatistic.UNKNOWN).setAvgSizeByte(width).build();
+=======
+        return new ColumnStatisticBuilder(ColumnStatistic.UNKNOWN)
+                .setCount(context.getRowCount())
+                .setAvgSizeByte(width)
+                .build();
+>>>>>>> f0f7c7eaed ([opt](nereids) refine expression estimation)
     }
 
     // TODO: return a proper estimated stat after supports histogram
@@ -432,6 +449,24 @@ public ColumnStatistic visitAggregateExpression(AggregateExpression aggregateExp
         return aggregateExpression.child().accept(this, context);
     }
 
+    @Override
+    public ColumnStatistic visitAggregateFunction(AggregateFunction aggregateExpression,
+            Statistics context) {
+        if (aggregateExpression.children().size() == 1) {
+            ColumnStatistic columnStat = aggregateExpression.child(0).accept(this, context);
+            if (columnStat.isUnKnown) {
+                return ColumnStatistic.UNKNOWN;
+            }
+            // by default reset min/max as invalid to avoid misused
+            return new ColumnStatisticBuilder(columnStat)
+                    .setMinExpr(null).setMinValue(Double.NEGATIVE_INFINITY)
+                    .setMaxExpr(null).setMaxValue(Double.POSITIVE_INFINITY)
+                    .build();
+        } else {
+            return visit(aggregateExpression, context);
+        }
+    }
+
     @Override
     public ColumnStatistic visitComparisonPredicate(ComparisonPredicate cp, Statistics context) {
         ColumnStatistic leftStats = cp.left().accept(this, context);
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 b3576a0e58e61e6..7a8a698713ac35e 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
@@ -334,7 +334,8 @@ private Statistics estimateEqualTo(ComparisonPredicate cp, ColumnStatistic stats
             } else {
                 double val = statsForRight.maxValue;
                 if (val > statsForLeft.maxValue || val < statsForLeft.minValue) {
-                    selectivity = 0.0;
+                    // do a lower bound protection to avoid using 0 directly
+                    selectivity = RANGE_SELECTIVITY_THRESHOLD;
                 } else if (ndv >= 1.0) {
                     selectivity = StatsMathUtil.minNonNaN(1.0, 1.0 / ndv);
                 } else {