diff --git a/expression/builtin_compare.go b/expression/builtin_compare.go
index dec5d06983679..bcb27a1233da7 100644
--- a/expression/builtin_compare.go
+++ b/expression/builtin_compare.go
@@ -1565,33 +1565,17 @@ 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
-	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 {
+		if MaybeOverOptimized4PlanCache(ctx, []Expression{arg1}) {
+			ctx.GetSessionVars().StmtCtx.SetSkipPlanCache(errors.Errorf("skip plan-cache: '%v' may be converted to INT", arg1.String()))
+			RemoveMutableConst(ctx, args)
+		}
+
 		arg1, isExceptional = RefineComparedConstant(ctx, *arg0Type, arg1, c.op)
 		// Why check not null flag
 		// eg: int_col > const_val(which is less than min_int32)
@@ -1619,6 +1603,11 @@ 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
@@ -1636,6 +1625,11 @@ 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)
@@ -1644,6 +1638,11 @@ 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 a2d1f242a0ff6..c7af8385d556c 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, []expression.Expression{c})
+					expression.RemoveMutableConst(er.sctx, args)
 				}
 				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 8acc28b7b0062..8788fa9b72c59 100644
--- a/planner/core/plan_cache_test.go
+++ b/planner/core/plan_cache_test.go
@@ -503,3 +503,22 @@ 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"))
+}