diff --git a/expression/builtin_compare.go b/expression/builtin_compare.go
index bcb27a1233da7..dec5d06983679 100644
--- a/expression/builtin_compare.go
+++ b/expression/builtin_compare.go
@@ -1565,17 +1565,33 @@ func (c *compareFunctionClass) refineArgs(ctx sessionctx.Context, args []Express
 	arg0Type, arg1Type := args[0].GetType(), args[1].GetType()
 	arg0IsInt := arg0Type.EvalType() == types.ETInt
 	arg1IsInt := arg1Type.EvalType() == types.ETInt
+	arg0IsString := arg0Type.EvalType() == types.ETString
+	arg1IsString := arg1Type.EvalType() == types.ETString
 	arg0, arg0IsCon := args[0].(*Constant)
 	arg1, arg1IsCon := args[1].(*Constant)
 	isExceptional, finalArg0, finalArg1 := false, args[0], args[1]
 	isPositiveInfinite, isNegativeInfinite := false, false
-	// int non-constant [cmp] non-int constant
-	if arg0IsInt && !arg0IsCon && !arg1IsInt && arg1IsCon {
-		if MaybeOverOptimized4PlanCache(ctx, []Expression{arg1}) {
-			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to INT", arg1.String()))
+	if MaybeOverOptimized4PlanCache(ctx, args) {
+		// To keep the result be compatible with MySQL, refine `int non-constant <cmp> str constant`
+		// here and skip this refine operation in all other cases for safety.
+		if (arg0IsInt && !arg0IsCon && arg1IsString && arg1IsCon) || (arg1IsInt && !arg1IsCon && arg0IsString && arg0IsCon) {
+			var reason error
+			if arg1IsString {
+				reason = errors.Errorf("skip plan-cache: '%v' may be converted to INT", arg1.String())
+			} else { // arg0IsString
+				reason = errors.Errorf("skip plan-cache: '%v' may be converted to INT", arg0.String())
+			}
+			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(reason)
 			RemoveMutableConst(ctx, args)
+		} else {
+			return args
 		}
-
+	} else if !ctx.GetSessionVars().StmtCtx.UseCache {
+		// We should remove the mutable constant for correctness, because its value may be changed.
+		RemoveMutableConst(ctx, args)
+	}
+	// int non-constant [cmp] non-int constant
+	if arg0IsInt && !arg0IsCon && !arg1IsInt && arg1IsCon {
 		arg1, isExceptional = RefineComparedConstant(ctx, *arg0Type, arg1, c.op)
 		// Why check not null flag
 		// eg: int_col > const_val(which is less than min_int32)
@@ -1603,11 +1619,6 @@ func (c *compareFunctionClass) refineArgs(ctx sessionctx.Context, args []Express
 	}
 	// non-int constant [cmp] int non-constant
 	if arg1IsInt && !arg1IsCon && !arg0IsInt && arg0IsCon {
-		if MaybeOverOptimized4PlanCache(ctx, []Expression{arg0}) {
-			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to INT", arg0.String()))
-			RemoveMutableConst(ctx, args)
-		}
-
 		arg0, isExceptional = RefineComparedConstant(ctx, *arg1Type, arg0, symmetricOp[c.op])
 		if !isExceptional || (isExceptional && mysql.HasNotNullFlag(arg1Type.GetFlag())) {
 			finalArg0 = arg0
@@ -1625,11 +1636,6 @@ func (c *compareFunctionClass) refineArgs(ctx sessionctx.Context, args []Express
 	}
 	// int constant [cmp] year type
 	if arg0IsCon && arg0IsInt && arg1Type.GetType() == mysql.TypeYear && !arg0.Value.IsNull() {
-		if MaybeOverOptimized4PlanCache(ctx, []Expression{arg0}) {
-			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to YEAR", arg0.String()))
-			RemoveMutableConst(ctx, args)
-		}
-
 		adjusted, failed := types.AdjustYear(arg0.Value.GetInt64(), false)
 		if failed == nil {
 			arg0.Value.SetInt64(adjusted)
@@ -1638,11 +1644,6 @@ func (c *compareFunctionClass) refineArgs(ctx sessionctx.Context, args []Express
 	}
 	// year type [cmp] int constant
 	if arg1IsCon && arg1IsInt && arg0Type.GetType() == mysql.TypeYear && !arg1.Value.IsNull() {
-		if MaybeOverOptimized4PlanCache(ctx, []Expression{arg1}) {
-			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to YEAR", arg1.String()))
-			RemoveMutableConst(ctx, args)
-		}
-
 		adjusted, failed := types.AdjustYear(arg1.Value.GetInt64(), false)
 		if failed == nil {
 			arg1.Value.SetInt64(adjusted)
diff --git a/planner/core/expression_rewriter.go b/planner/core/expression_rewriter.go
index c7af8385d556c..a2d1f242a0ff6 100644
--- a/planner/core/expression_rewriter.go
+++ b/planner/core/expression_rewriter.go
@@ -1563,7 +1563,7 @@ func (er *expressionRewriter) inToExpression(lLen int, not bool, tp *types.Field
 						continue // no need to refine it
 					}
 					er.sctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to INT", c.String()))
-					expression.RemoveMutableConst(er.sctx, args)
+					expression.RemoveMutableConst(er.sctx, []expression.Expression{c})
 				}
 				args[i], isExceptional = expression.RefineComparedConstant(er.sctx, *leftFt, c, opcode.EQ)
 				if isExceptional {
diff --git a/planner/core/plan_cache_test.go b/planner/core/plan_cache_test.go
index e3a0d276e9815..8278050681553 100644
--- a/planner/core/plan_cache_test.go
+++ b/planner/core/plan_cache_test.go
@@ -506,22 +506,3 @@ func TestPlanCacheWithLimit(t *testing.T) {
 	tk.MustExec("execute stmt using @a")
 	tk.MustQuery("show warnings").Check(testkit.Rows("Warning 1105 skip plan-cache: limit count more than 10000"))
 }
-
-func TestIssue40679(t *testing.T) {
-	store := testkit.CreateMockStore(t)
-	tk := testkit.NewTestKit(t, store)
-	tk.MustExec("use test")
-	tk.MustExec("create table t (a int, key(a));")
-	tk.MustExec("prepare st from 'select * from t use index(a) where a < ?'")
-	tk.MustExec("set @a1=1.1")
-	tk.MustExec("execute st using @a1")
-
-	tkProcess := tk.Session().ShowProcess()
-	ps := []*util.ProcessInfo{tkProcess}
-	tk.Session().SetSessionManager(&testkit.MockSessionManager{PS: ps})
-	rows := tk.MustQuery(fmt.Sprintf("explain for connection %d", tkProcess.ID)).Rows()
-	require.True(t, strings.Contains(rows[1][0].(string), "RangeScan")) // RangeScan not FullScan
-
-	tk.MustExec("execute st using @a1")
-	tk.MustQuery("show warnings").Check(testkit.Rows("Warning 1105 skip plan-cache: '1.1' may be converted to INT"))
-}