diff --git a/expression/expr_to_pb.go b/expression/expr_to_pb.go
index a56498e88e6da..515b2f5f13795 100644
--- a/expression/expr_to_pb.go
+++ b/expression/expr_to_pb.go
@@ -309,10 +309,14 @@ func (pc PbConverter) canFuncBePushed(sf *ScalarFunction) bool {
 		// op functions.
 		ast.LogicAnd,
 		ast.LogicOr,
+		ast.LogicXor,
 		ast.UnaryNot,
 		ast.And,
 		ast.Or,
+		ast.Xor,
 		ast.BitNeg,
+		ast.LeftShift,
+		ast.RightShift,
 
 		// compare functions.
 		ast.LT,
@@ -347,9 +351,16 @@ func (pc PbConverter) canFuncBePushed(sf *ScalarFunction) bool {
 		ast.Log10,
 		ast.Exp,
 		ast.Sin,
+		ast.Asin,
 		ast.Cos,
+		ast.Acos,
 		ast.Tan,
+		ast.Atan,
+		ast.Atan2,
 		ast.Cot,
+		ast.Radians,
+		ast.Degrees,
+		ast.CRC32,
 
 		// control flow functions.
 		ast.Case,
@@ -359,6 +370,14 @@ func (pc PbConverter) canFuncBePushed(sf *ScalarFunction) bool {
 
 		// string functions.
 		ast.Length,
+		ast.BitLength,
+		ast.Concat,
+		ast.Locate,
+		ast.ASCII,
+		ast.Reverse,
+		ast.LTrim,
+		ast.RTrim,
+		ast.Left,
 
 		// json functions.
 		ast.JSONType,
diff --git a/expression/expr_to_pb_test.go b/expression/expr_to_pb_test.go
index 1806c0dfdfd09..e8b4116cbd5f8 100644
--- a/expression/expr_to_pb_test.go
+++ b/expression/expr_to_pb_test.go
@@ -388,7 +388,7 @@ func (s *testEvaluatorSuite) TestLogicalFunc2Pb(c *C) {
 	jsons := []string{
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3101,\"field_type\":{\"tp\":8,\"flag\":128,\"flen\":1,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3102,\"field_type\":{\"tp\":8,\"flag\":128,\"flen\":1,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
-		"null",
+		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3103,\"field_type\":{\"tp\":8,\"flag\":128,\"flen\":1,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":1,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3104,\"field_type\":{\"tp\":8,\"flag\":128,\"flen\":1,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 	}
 	for i, pbExpr := range pbExprs {
@@ -424,9 +424,9 @@ func (s *testEvaluatorSuite) TestBitwiseFunc2Pb(c *C) {
 	jsons := []string{
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3118,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3119,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
-		"null",
-		"null",
-		"null",
+		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3120,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
+		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3129,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
+		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}},{\"tp\":201,\"val\":\"gAAAAAAAAAI=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3130,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 		"{\"tp\":10000,\"children\":[{\"tp\":201,\"val\":\"gAAAAAAAAAE=\",\"sig\":0,\"field_type\":{\"tp\":3,\"flag\":0,\"flen\":-1,\"decimal\":-1,\"collate\":46,\"charset\":\"\"}}],\"sig\":3121,\"field_type\":{\"tp\":8,\"flag\":160,\"flen\":20,\"decimal\":0,\"collate\":63,\"charset\":\"binary\"}}",
 	}
 	for i, pbExpr := range pbExprs {