diff --git a/compiler/rustc_typeck/src/check/op.rs b/compiler/rustc_typeck/src/check/op.rs
index fa0fac93276..c269a9a0c46 100644
--- a/compiler/rustc_typeck/src/check/op.rs
+++ b/compiler/rustc_typeck/src/check/op.rs
@@ -11,6 +11,7 @@ use rustc_infer::traits::ObligationCauseCode;
 use rustc_middle::ty::adjustment::{
     Adjust, Adjustment, AllowTwoPhase, AutoBorrow, AutoBorrowMutability,
 };
+use rustc_middle::ty::print::with_no_trimmed_paths;
 use rustc_middle::ty::{
     self, Ty, TyCtxt, TypeFolder, TypeSuperFoldable, TypeSuperVisitable, TypeVisitable, TypeVisitor,
 };
@@ -313,7 +314,10 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
             // error types are considered "builtin"
             Err(_) if lhs_ty.references_error() || rhs_ty.references_error() => self.tcx.ty_error(),
             Err(errors) => {
-                let (mut err, missing_trait, use_output) = match is_assign {
+                let (_, item) = lang_item_for_op(self.tcx, Op::Binary(op, is_assign), op.span);
+                let missing_trait =
+                    item.map(|def_id| with_no_trimmed_paths!(self.tcx.def_path_str(def_id)));
+                let (mut err, use_output) = match is_assign {
                     IsAssign::Yes => {
                         let mut err = struct_span_err!(
                             self.tcx.sess,
@@ -327,112 +331,60 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
                             lhs_expr.span,
                             format!("cannot use `{}=` on type `{}`", op.node.as_str(), lhs_ty),
                         );
-                        let missing_trait = match op.node {
-                            hir::BinOpKind::Add => Some("std::ops::AddAssign"),
-                            hir::BinOpKind::Sub => Some("std::ops::SubAssign"),
-                            hir::BinOpKind::Mul => Some("std::ops::MulAssign"),
-                            hir::BinOpKind::Div => Some("std::ops::DivAssign"),
-                            hir::BinOpKind::Rem => Some("std::ops::RemAssign"),
-                            hir::BinOpKind::BitAnd => Some("std::ops::BitAndAssign"),
-                            hir::BinOpKind::BitXor => Some("std::ops::BitXorAssign"),
-                            hir::BinOpKind::BitOr => Some("std::ops::BitOrAssign"),
-                            hir::BinOpKind::Shl => Some("std::ops::ShlAssign"),
-                            hir::BinOpKind::Shr => Some("std::ops::ShrAssign"),
-                            _ => None,
-                        };
                         self.note_unmet_impls_on_type(&mut err, errors);
-                        (err, missing_trait, false)
+                        (err, false)
                     }
                     IsAssign::No => {
-                        let (message, missing_trait, use_output) = match op.node {
-                            hir::BinOpKind::Add => (
-                                format!("cannot add `{rhs_ty}` to `{lhs_ty}`"),
-                                Some("std::ops::Add"),
-                                true,
-                            ),
-                            hir::BinOpKind::Sub => (
-                                format!("cannot subtract `{rhs_ty}` from `{lhs_ty}`"),
-                                Some("std::ops::Sub"),
-                                true,
-                            ),
-                            hir::BinOpKind::Mul => (
-                                format!("cannot multiply `{lhs_ty}` by `{rhs_ty}`"),
-                                Some("std::ops::Mul"),
-                                true,
-                            ),
-                            hir::BinOpKind::Div => (
-                                format!("cannot divide `{lhs_ty}` by `{rhs_ty}`"),
-                                Some("std::ops::Div"),
-                                true,
-                            ),
-                            hir::BinOpKind::Rem => (
-                                format!("cannot mod `{lhs_ty}` by `{rhs_ty}`"),
-                                Some("std::ops::Rem"),
-                                true,
-                            ),
-                            hir::BinOpKind::BitAnd => (
-                                format!("no implementation for `{lhs_ty} & {rhs_ty}`"),
-                                Some("std::ops::BitAnd"),
-                                true,
-                            ),
-                            hir::BinOpKind::BitXor => (
-                                format!("no implementation for `{lhs_ty} ^ {rhs_ty}`"),
-                                Some("std::ops::BitXor"),
-                                true,
-                            ),
-                            hir::BinOpKind::BitOr => (
-                                format!("no implementation for `{lhs_ty} | {rhs_ty}`"),
-                                Some("std::ops::BitOr"),
-                                true,
-                            ),
-                            hir::BinOpKind::Shl => (
-                                format!("no implementation for `{lhs_ty} << {rhs_ty}`"),
-                                Some("std::ops::Shl"),
-                                true,
-                            ),
-                            hir::BinOpKind::Shr => (
-                                format!("no implementation for `{lhs_ty} >> {rhs_ty}`"),
-                                Some("std::ops::Shr"),
-                                true,
-                            ),
-                            hir::BinOpKind::Eq | hir::BinOpKind::Ne => (
-                                format!(
-                                    "binary operation `{}` cannot be applied to type `{}`",
-                                    op.node.as_str(),
-                                    lhs_ty
-                                ),
-                                Some("std::cmp::PartialEq"),
-                                false,
-                            ),
-                            hir::BinOpKind::Lt
-                            | hir::BinOpKind::Le
-                            | hir::BinOpKind::Gt
-                            | hir::BinOpKind::Ge => (
-                                format!(
-                                    "binary operation `{}` cannot be applied to type `{}`",
-                                    op.node.as_str(),
-                                    lhs_ty
-                                ),
-                                Some("std::cmp::PartialOrd"),
-                                false,
-                            ),
-                            _ => (
-                                format!(
-                                    "binary operation `{}` cannot be applied to type `{}`",
-                                    op.node.as_str(),
-                                    lhs_ty
-                                ),
-                                None,
-                                false,
+                        let message = match op.node {
+                            hir::BinOpKind::Add => {
+                                format!("cannot add `{rhs_ty}` to `{lhs_ty}`")
+                            }
+                            hir::BinOpKind::Sub => {
+                                format!("cannot subtract `{rhs_ty}` from `{lhs_ty}`")
+                            }
+                            hir::BinOpKind::Mul => {
+                                format!("cannot multiply `{lhs_ty}` by `{rhs_ty}`")
+                            }
+                            hir::BinOpKind::Div => {
+                                format!("cannot divide `{lhs_ty}` by `{rhs_ty}`")
+                            }
+                            hir::BinOpKind::Rem => {
+                                format!("cannot mod `{lhs_ty}` by `{rhs_ty}`")
+                            }
+                            hir::BinOpKind::BitAnd => {
+                                format!("no implementation for `{lhs_ty} & {rhs_ty}`")
+                            }
+                            hir::BinOpKind::BitXor => {
+                                format!("no implementation for `{lhs_ty} ^ {rhs_ty}`")
+                            }
+                            hir::BinOpKind::BitOr => {
+                                format!("no implementation for `{lhs_ty} | {rhs_ty}`")
+                            }
+                            hir::BinOpKind::Shl => {
+                                format!("no implementation for `{lhs_ty} << {rhs_ty}`")
+                            }
+                            hir::BinOpKind::Shr => {
+                                format!("no implementation for `{lhs_ty} >> {rhs_ty}`")
+                            }
+                            _ => format!(
+                                "binary operation `{}` cannot be applied to type `{}`",
+                                op.node.as_str(),
+                                lhs_ty
                             ),
                         };
+                        let use_output = item.map_or(false, |def_id| {
+                            self.tcx.associated_item_def_ids(def_id).iter().any(|item_def_id| {
+                                self.tcx.opt_associated_item(*item_def_id).unwrap().name
+                                    == sym::Output
+                            })
+                        });
                         let mut err = struct_span_err!(self.tcx.sess, op.span, E0369, "{message}");
                         if !lhs_expr.span.eq(&rhs_expr.span) {
                             err.span_label(lhs_expr.span, lhs_ty.to_string());
                             err.span_label(rhs_expr.span, rhs_ty.to_string());
                         }
                         self.note_unmet_impls_on_type(&mut err, errors);
-                        (err, missing_trait, use_output)
+                        (err, use_output)
                     }
                 };
 
@@ -773,64 +725,11 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
         op: Op,
         expected: Expectation<'tcx>,
     ) -> Result<MethodCallee<'tcx>, Vec<FulfillmentError<'tcx>>> {
-        let lang = self.tcx.lang_items();
-
         let span = match op {
             Op::Binary(op, _) => op.span,
             Op::Unary(_, span) => span,
         };
-        let (opname, trait_did) = if let Op::Binary(op, IsAssign::Yes) = op {
-            match op.node {
-                hir::BinOpKind::Add => (sym::add_assign, lang.add_assign_trait()),
-                hir::BinOpKind::Sub => (sym::sub_assign, lang.sub_assign_trait()),
-                hir::BinOpKind::Mul => (sym::mul_assign, lang.mul_assign_trait()),
-                hir::BinOpKind::Div => (sym::div_assign, lang.div_assign_trait()),
-                hir::BinOpKind::Rem => (sym::rem_assign, lang.rem_assign_trait()),
-                hir::BinOpKind::BitXor => (sym::bitxor_assign, lang.bitxor_assign_trait()),
-                hir::BinOpKind::BitAnd => (sym::bitand_assign, lang.bitand_assign_trait()),
-                hir::BinOpKind::BitOr => (sym::bitor_assign, lang.bitor_assign_trait()),
-                hir::BinOpKind::Shl => (sym::shl_assign, lang.shl_assign_trait()),
-                hir::BinOpKind::Shr => (sym::shr_assign, lang.shr_assign_trait()),
-                hir::BinOpKind::Lt
-                | hir::BinOpKind::Le
-                | hir::BinOpKind::Ge
-                | hir::BinOpKind::Gt
-                | hir::BinOpKind::Eq
-                | hir::BinOpKind::Ne
-                | hir::BinOpKind::And
-                | hir::BinOpKind::Or => {
-                    span_bug!(span, "impossible assignment operation: {}=", op.node.as_str())
-                }
-            }
-        } else if let Op::Binary(op, IsAssign::No) = op {
-            match op.node {
-                hir::BinOpKind::Add => (sym::add, lang.add_trait()),
-                hir::BinOpKind::Sub => (sym::sub, lang.sub_trait()),
-                hir::BinOpKind::Mul => (sym::mul, lang.mul_trait()),
-                hir::BinOpKind::Div => (sym::div, lang.div_trait()),
-                hir::BinOpKind::Rem => (sym::rem, lang.rem_trait()),
-                hir::BinOpKind::BitXor => (sym::bitxor, lang.bitxor_trait()),
-                hir::BinOpKind::BitAnd => (sym::bitand, lang.bitand_trait()),
-                hir::BinOpKind::BitOr => (sym::bitor, lang.bitor_trait()),
-                hir::BinOpKind::Shl => (sym::shl, lang.shl_trait()),
-                hir::BinOpKind::Shr => (sym::shr, lang.shr_trait()),
-                hir::BinOpKind::Lt => (sym::lt, lang.partial_ord_trait()),
-                hir::BinOpKind::Le => (sym::le, lang.partial_ord_trait()),
-                hir::BinOpKind::Ge => (sym::ge, lang.partial_ord_trait()),
-                hir::BinOpKind::Gt => (sym::gt, lang.partial_ord_trait()),
-                hir::BinOpKind::Eq => (sym::eq, lang.eq_trait()),
-                hir::BinOpKind::Ne => (sym::ne, lang.eq_trait()),
-                hir::BinOpKind::And | hir::BinOpKind::Or => {
-                    span_bug!(span, "&& and || are not overloadable")
-                }
-            }
-        } else if let Op::Unary(hir::UnOp::Not, _) = op {
-            (sym::not, lang.not_trait())
-        } else if let Op::Unary(hir::UnOp::Neg, _) = op {
-            (sym::neg, lang.neg_trait())
-        } else {
-            bug!("lookup_op_method: op not supported: {:?}", op)
-        };
+        let (opname, trait_did) = lang_item_for_op(self.tcx, op, span);
 
         debug!(
             "lookup_op_method(lhs_ty={:?}, op={:?}, opname={:?}, trait_did={:?})",
@@ -891,6 +790,66 @@ impl<'a, 'tcx> FnCtxt<'a, 'tcx> {
     }
 }
 
+fn lang_item_for_op(
+    tcx: TyCtxt<'_>,
+    op: Op,
+    span: Span,
+) -> (rustc_span::Symbol, Option<hir::def_id::DefId>) {
+    let lang = tcx.lang_items();
+    if let Op::Binary(op, IsAssign::Yes) = op {
+        match op.node {
+            hir::BinOpKind::Add => (sym::add_assign, lang.add_assign_trait()),
+            hir::BinOpKind::Sub => (sym::sub_assign, lang.sub_assign_trait()),
+            hir::BinOpKind::Mul => (sym::mul_assign, lang.mul_assign_trait()),
+            hir::BinOpKind::Div => (sym::div_assign, lang.div_assign_trait()),
+            hir::BinOpKind::Rem => (sym::rem_assign, lang.rem_assign_trait()),
+            hir::BinOpKind::BitXor => (sym::bitxor_assign, lang.bitxor_assign_trait()),
+            hir::BinOpKind::BitAnd => (sym::bitand_assign, lang.bitand_assign_trait()),
+            hir::BinOpKind::BitOr => (sym::bitor_assign, lang.bitor_assign_trait()),
+            hir::BinOpKind::Shl => (sym::shl_assign, lang.shl_assign_trait()),
+            hir::BinOpKind::Shr => (sym::shr_assign, lang.shr_assign_trait()),
+            hir::BinOpKind::Lt
+            | hir::BinOpKind::Le
+            | hir::BinOpKind::Ge
+            | hir::BinOpKind::Gt
+            | hir::BinOpKind::Eq
+            | hir::BinOpKind::Ne
+            | hir::BinOpKind::And
+            | hir::BinOpKind::Or => {
+                span_bug!(span, "impossible assignment operation: {}=", op.node.as_str())
+            }
+        }
+    } else if let Op::Binary(op, IsAssign::No) = op {
+        match op.node {
+            hir::BinOpKind::Add => (sym::add, lang.add_trait()),
+            hir::BinOpKind::Sub => (sym::sub, lang.sub_trait()),
+            hir::BinOpKind::Mul => (sym::mul, lang.mul_trait()),
+            hir::BinOpKind::Div => (sym::div, lang.div_trait()),
+            hir::BinOpKind::Rem => (sym::rem, lang.rem_trait()),
+            hir::BinOpKind::BitXor => (sym::bitxor, lang.bitxor_trait()),
+            hir::BinOpKind::BitAnd => (sym::bitand, lang.bitand_trait()),
+            hir::BinOpKind::BitOr => (sym::bitor, lang.bitor_trait()),
+            hir::BinOpKind::Shl => (sym::shl, lang.shl_trait()),
+            hir::BinOpKind::Shr => (sym::shr, lang.shr_trait()),
+            hir::BinOpKind::Lt => (sym::lt, lang.partial_ord_trait()),
+            hir::BinOpKind::Le => (sym::le, lang.partial_ord_trait()),
+            hir::BinOpKind::Ge => (sym::ge, lang.partial_ord_trait()),
+            hir::BinOpKind::Gt => (sym::gt, lang.partial_ord_trait()),
+            hir::BinOpKind::Eq => (sym::eq, lang.eq_trait()),
+            hir::BinOpKind::Ne => (sym::ne, lang.eq_trait()),
+            hir::BinOpKind::And | hir::BinOpKind::Or => {
+                span_bug!(span, "&& and || are not overloadable")
+            }
+        }
+    } else if let Op::Unary(hir::UnOp::Not, _) = op {
+        (sym::not, lang.not_trait())
+    } else if let Op::Unary(hir::UnOp::Neg, _) = op {
+        (sym::neg, lang.neg_trait())
+    } else {
+        bug!("lookup_op_method: op not supported: {:?}", op)
+    }
+}
+
 // Binary operator categories. These categories summarize the behavior
 // with respect to the builtin operations supported.
 enum BinOpCategory {