diff --git a/pkg/runtime/function/exp_test.go b/pkg/runtime/function/exp_test.go
index 7fd42976..27a10d66 100644
--- a/pkg/runtime/function/exp_test.go
+++ b/pkg/runtime/function/exp_test.go
@@ -59,3 +59,24 @@ func TestExp(t *testing.T) {
 		})
 	}
 }
+
+func TestExp_Error(t *testing.T) {
+	fn := proto.MustGetFunc(FuncExp)
+	assert.Equal(t, 1, fn.NumInput())
+
+	type tt struct {
+		desc string
+		in   proto.Value
+		out  float64
+	}
+
+	for _, it := range []tt{
+		{"EXP(Nil)", nil, 1},
+	} {
+		t.Run(it.desc, func(t *testing.T) {
+			out, err := fn.Apply(context.Background(), proto.ToValuer(it.in))
+			assert.Nil(t, err)
+			assert.Nil(t, out)
+		})
+	}
+}
diff --git a/pkg/runtime/function/first_value_test.go b/pkg/runtime/function/first_value_test.go
index 41852c7d..728e10d1 100644
--- a/pkg/runtime/function/first_value_test.go
+++ b/pkg/runtime/function/first_value_test.go
@@ -33,6 +33,8 @@ import (
 
 func TestFuncFirstValue(t *testing.T) {
 	fn := proto.MustGetFunc(FuncFirstValue)
+	assert.Equal(t, 0, fn.NumInput())
+
 	type tt struct {
 		inputs [][]proto.Value
 		want   string
@@ -182,6 +184,19 @@ func TestFuncFirstValue(t *testing.T) {
 			},
 			"0",
 		},
+		{
+			[][]proto.Value{
+				{proto.NewValueString("08:00:00"), proto.NewValueString("xh458")},
+			},
+			"",
+		},
+		{
+			[][]proto.Value{
+				// order column, partition column, value column
+				{proto.NewValueString("07:00:00"), proto.NewValueString("st113"), proto.NewValueFloat64(10)},
+			},
+			"10",
+		},
 	} {
 		t.Run(v.want, func(t *testing.T) {
 			var inputs []proto.Valuer
@@ -196,3 +211,37 @@ func TestFuncFirstValue(t *testing.T) {
 		})
 	}
 }
+
+func TestFuncFirstValue_Error(t *testing.T) {
+	fn := proto.MustGetFunc(FuncFirstValue)
+	assert.Equal(t, 0, fn.NumInput())
+
+	type tt struct {
+		inputs []proto.Value
+		want   string
+	}
+	for _, v := range []tt{
+		{
+			[]proto.Value{
+				proto.NewValueString("07:00:00"), nil, proto.NewValueFloat64(10),
+			},
+			"",
+		},
+		{
+			[]proto.Value{
+				proto.NewValueString("07:00:00"), proto.NewValueString("st113"), nil,
+			},
+			"",
+		},
+	} {
+		t.Run(v.want, func(t *testing.T) {
+			var inputs []proto.Valuer
+			for i := range v.inputs {
+				inputs = append(inputs, proto.ToValuer(v.inputs[i]))
+			}
+			out, err := fn.Apply(context.Background(), inputs...)
+			assert.NoError(t, err)
+			assert.Nil(t, out)
+		})
+	}
+}
diff --git a/pkg/runtime/function/floor_test.go b/pkg/runtime/function/floor_test.go
index eedbd61b..2170467c 100644
--- a/pkg/runtime/function/floor_test.go
+++ b/pkg/runtime/function/floor_test.go
@@ -58,3 +58,23 @@ func TestFloor(t *testing.T) {
 		})
 	}
 }
+
+func TestFloor_Error(t *testing.T) {
+	fn := proto.MustGetFunc(FuncFloor)
+	assert.Equal(t, 1, fn.NumInput())
+
+	type tt struct {
+		in  proto.Value
+		out string
+	}
+
+	for _, it := range []tt{
+		{nil, ""},
+	} {
+		t.Run(it.out, func(t *testing.T) {
+			out, err := fn.Apply(context.Background(), proto.ToValuer(it.in))
+			assert.NoError(t, err)
+			assert.Nil(t, out)
+		})
+	}
+}
diff --git a/pkg/runtime/function/format_bytes_test.go b/pkg/runtime/function/format_bytes_test.go
index 032e2db8..1a889b10 100644
--- a/pkg/runtime/function/format_bytes_test.go
+++ b/pkg/runtime/function/format_bytes_test.go
@@ -60,3 +60,58 @@ func TestFormatBytes(t *testing.T) {
 		})
 	}
 }
+
+func TestFormatBytes_Nil(t *testing.T) {
+	fn := proto.MustGetFunc(FuncFormatBytes)
+	assert.Equal(t, 1, fn.NumInput())
+
+	out, err := fn.Apply(context.TODO(), proto.ToValuer(nil))
+	assert.NoError(t, err)
+	assert.Nil(t, out)
+
+	type tt struct {
+		name   string
+		input  interface{}
+		output string
+	}
+
+	for _, next := range []tt{
+		{"Test_Nil", nil, "512 bytes"},
+	} {
+		t.Run(fmt.Sprint(next.name), func(t *testing.T) {
+			val, err := proto.NewValue(next.input)
+			assert.NoError(t, err)
+			actual, err := fn.Apply(context.TODO(), proto.ToValuer(val))
+			assert.NoError(t, err)
+			assert.Nil(t, actual)
+		})
+	}
+}
+
+func TestFormatBytes_Error(t *testing.T) {
+	fn := proto.MustGetFunc(FuncFormatBytes)
+	assert.Equal(t, 1, fn.NumInput())
+
+	out, err := fn.Apply(context.TODO(), proto.ToValuer(nil))
+	assert.NoError(t, err)
+	assert.Nil(t, out)
+
+	type tt struct {
+		name   string
+		input  interface{}
+		output string
+	}
+
+	for _, next := range []tt{
+		{"Test_Error", "a", "0 bytes"},
+		{"Test_Error", "0", "0 bytes"},
+	} {
+		t.Run(fmt.Sprint(next.name), func(t *testing.T) {
+			val, err := proto.NewValue(next.input)
+			assert.NoError(t, err)
+			actual, err := fn.Apply(context.TODO(), proto.ToValuer(val))
+			assert.NoError(t, err)
+			assert.Equal(t, next.output, actual.String())
+		})
+	}
+}