diff --git a/clippy_lints/src/operators/arithmetic_side_effects.rs b/clippy_lints/src/operators/arithmetic_side_effects.rs
index d871b72db8f..fc2a828bfc0 100644
--- a/clippy_lints/src/operators/arithmetic_side_effects.rs
+++ b/clippy_lints/src/operators/arithmetic_side_effects.rs
@@ -9,6 +9,7 @@ use rustc_ast as ast;
 use rustc_data_structures::fx::FxHashSet;
 use rustc_hir as hir;
 use rustc_lint::{LateContext, LateLintPass};
+use rustc_middle::ty::Ty;
 use rustc_session::impl_lint_pass;
 use rustc_span::source_map::{Span, Spanned};
 
@@ -67,20 +68,14 @@ impl ArithmeticSideEffects {
     }
 
     /// Checks if the given `expr` has any of the inner `allowed` elements.
-    fn is_allowed_ty(&self, cx: &LateContext<'_>, expr: &hir::Expr<'_>) -> bool {
-        self.allowed.contains(
-            cx.typeck_results()
-                .expr_ty(expr)
-                .to_string()
-                .split('<')
-                .next()
-                .unwrap_or_default(),
-        )
+    fn is_allowed_ty(&self, ty: Ty<'_>) -> bool {
+        self.allowed
+            .contains(ty.to_string().split('<').next().unwrap_or_default())
     }
 
     // For example, 8i32 or &i64::MAX.
-    fn is_integral<'expr, 'tcx>(cx: &LateContext<'tcx>, expr: &'expr hir::Expr<'tcx>) -> bool {
-        cx.typeck_results().expr_ty(expr).peel_refs().is_integral()
+    fn is_integral(ty: Ty<'_>) -> bool {
+        ty.peel_refs().is_integral()
     }
 
     // Common entry-point to avoid code duplication.
@@ -129,10 +124,13 @@ impl ArithmeticSideEffects {
         ) {
             return;
         };
-        if self.is_allowed_ty(cx, lhs) && self.is_allowed_ty(cx, rhs) {
+        let lhs_ty = cx.typeck_results().expr_ty(lhs);
+        let rhs_ty = cx.typeck_results().expr_ty(rhs);
+        let lhs_and_rhs_have_the_same_ty = lhs_ty == rhs_ty;
+        if lhs_and_rhs_have_the_same_ty && self.is_allowed_ty(lhs_ty) && self.is_allowed_ty(rhs_ty) {
             return;
         }
-        let has_valid_op = if Self::is_integral(cx, lhs) && Self::is_integral(cx, rhs) {
+        let has_valid_op = if Self::is_integral(lhs_ty) && Self::is_integral(rhs_ty) {
             match (Self::literal_integer(lhs), Self::literal_integer(rhs)) {
                 (None, None) => false,
                 (None, Some(local_expr)) => Self::has_valid_op(op, local_expr),
diff --git a/tests/ui/arithmetic_side_effects.stderr b/tests/ui/arithmetic_side_effects.stderr
index 7870c942e7d..8cabd05c2f9 100644
--- a/tests/ui/arithmetic_side_effects.stderr
+++ b/tests/ui/arithmetic_side_effects.stderr
@@ -1,10 +1,28 @@
+error: arithmetic operation that can potentially result in unexpected side-effects
+  --> $DIR/arithmetic_side_effects.rs:78:13
+   |
+LL |     let _ = String::new() + "";
+   |             ^^^^^^^^^^^^^^^^^^
+   |
+   = note: `-D clippy::arithmetic-side-effects` implied by `-D warnings`
+
+error: arithmetic operation that can potentially result in unexpected side-effects
+  --> $DIR/arithmetic_side_effects.rs:86:27
+   |
+LL |     let inferred_string = string + "";
+   |                           ^^^^^^^^^^^
+
+error: arithmetic operation that can potentially result in unexpected side-effects
+  --> $DIR/arithmetic_side_effects.rs:90:13
+   |
+LL |     let _ = inferred_string + "";
+   |             ^^^^^^^^^^^^^^^^^^^^
+
 error: arithmetic operation that can potentially result in unexpected side-effects
   --> $DIR/arithmetic_side_effects.rs:162:5
    |
 LL |     _n += 1;
    |     ^^^^^^^
-   |
-   = note: `-D clippy::arithmetic-side-effects` implied by `-D warnings`
 
 error: arithmetic operation that can potentially result in unexpected side-effects
   --> $DIR/arithmetic_side_effects.rs:163:5
@@ -312,5 +330,5 @@ error: arithmetic operation that can potentially result in unexpected side-effec
 LL |     _n = -&_n;
    |          ^^^^
 
-error: aborting due to 52 previous errors
+error: aborting due to 55 previous errors