diff --git a/library/core/src/cmp.rs b/library/core/src/cmp.rs
index 949896e574806..47ea199a835c5 100644
--- a/library/core/src/cmp.rs
+++ b/library/core/src/cmp.rs
@@ -360,12 +360,18 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_eq(), true);
     /// assert_eq!(Ordering::Greater.is_eq(), false);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_eq(self) -> bool {
-        matches!(self, Equal)
+        // Implementation note: It appears (as of 2022-12) that LLVM has an
+        // easier time with a comparison against zero like this, as opposed
+        // to looking for the `Less` value (-1) specifically, maybe because
+        // it's not always obvious to it that -2 isn't possible.
+        // Thus this and its siblings below are written this way, rather
+        // than the potentially-more-obvious `matches!` version.
+        (self as i8) == 0
     }
 
     /// Returns `true` if the ordering is not the `Equal` variant.
@@ -379,12 +385,12 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_ne(), false);
     /// assert_eq!(Ordering::Greater.is_ne(), true);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_ne(self) -> bool {
-        !matches!(self, Equal)
+        (self as i8) != 0
     }
 
     /// Returns `true` if the ordering is the `Less` variant.
@@ -398,12 +404,12 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_lt(), false);
     /// assert_eq!(Ordering::Greater.is_lt(), false);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_lt(self) -> bool {
-        matches!(self, Less)
+        (self as i8) < 0
     }
 
     /// Returns `true` if the ordering is the `Greater` variant.
@@ -417,12 +423,12 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_gt(), false);
     /// assert_eq!(Ordering::Greater.is_gt(), true);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_gt(self) -> bool {
-        matches!(self, Greater)
+        (self as i8) > 0
     }
 
     /// Returns `true` if the ordering is either the `Less` or `Equal` variant.
@@ -436,12 +442,12 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_le(), true);
     /// assert_eq!(Ordering::Greater.is_le(), false);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_le(self) -> bool {
-        !matches!(self, Greater)
+        (self as i8) <= 0
     }
 
     /// Returns `true` if the ordering is either the `Greater` or `Equal` variant.
@@ -455,12 +461,12 @@ impl Ordering {
     /// assert_eq!(Ordering::Equal.is_ge(), true);
     /// assert_eq!(Ordering::Greater.is_ge(), true);
     /// ```
-    #[inline]
+    #[inline(always)]
     #[must_use]
     #[rustc_const_stable(feature = "ordering_helpers", since = "1.53.0")]
     #[stable(feature = "ordering_helpers", since = "1.53.0")]
     pub const fn is_ge(self) -> bool {
-        !matches!(self, Less)
+        (self as i8) >= 0
     }
 
     /// Reverses the `Ordering`.
@@ -1124,7 +1130,7 @@ pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
     #[must_use]
     #[stable(feature = "rust1", since = "1.0.0")]
     fn lt(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Less))
+        if let Some(ordering) = self.partial_cmp(other) { ordering.is_lt() } else { false }
     }
 
     /// This method tests less than or equal to (for `self` and `other`) and is used by the `<=`
@@ -1143,7 +1149,7 @@ pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
     #[must_use]
     #[stable(feature = "rust1", since = "1.0.0")]
     fn le(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Less | Equal))
+        if let Some(ordering) = self.partial_cmp(other) { ordering.is_le() } else { false }
     }
 
     /// This method tests greater than (for `self` and `other`) and is used by the `>` operator.
@@ -1161,7 +1167,7 @@ pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
     #[must_use]
     #[stable(feature = "rust1", since = "1.0.0")]
     fn gt(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Greater))
+        if let Some(ordering) = self.partial_cmp(other) { ordering.is_gt() } else { false }
     }
 
     /// This method tests greater than or equal to (for `self` and `other`) and is used by the `>=`
@@ -1180,7 +1186,7 @@ pub trait PartialOrd<Rhs: ?Sized = Self>: PartialEq<Rhs> {
     #[must_use]
     #[stable(feature = "rust1", since = "1.0.0")]
     fn ge(&self, other: &Rhs) -> bool {
-        matches!(self.partial_cmp(other), Some(Greater | Equal))
+        if let Some(ordering) = self.partial_cmp(other) { ordering.is_ge() } else { false }
     }
 }
 
diff --git a/src/test/codegen/newtype-relational-operators.rs b/src/test/codegen/newtype-relational-operators.rs
new file mode 100644
index 0000000000000..5cf6c3ac0a233
--- /dev/null
+++ b/src/test/codegen/newtype-relational-operators.rs
@@ -0,0 +1,49 @@
+// The `derive(PartialOrd)` for a newtype doesn't override `lt`/`le`/`gt`/`ge`.
+// This double-checks that the `Option<Ordering>` intermediate values used
+// in the operators for such a type all optimize away.
+
+// compile-flags: -C opt-level=1
+// min-llvm-version: 15.0
+
+#![crate_type = "lib"]
+
+use std::cmp::Ordering;
+
+#[derive(PartialOrd, PartialEq)]
+pub struct Foo(u16);
+
+// CHECK-LABEL: @check_lt
+// CHECK-SAME: (i16 %[[A:.+]], i16 %[[B:.+]])
+#[no_mangle]
+pub fn check_lt(a: Foo, b: Foo) -> bool {
+    // CHECK: %[[R:.+]] = icmp ult i16 %[[A]], %[[B]]
+    // CHECK-NEXT: ret i1 %[[R]]
+    a < b
+}
+
+// CHECK-LABEL: @check_le
+// CHECK-SAME: (i16 %[[A:.+]], i16 %[[B:.+]])
+#[no_mangle]
+pub fn check_le(a: Foo, b: Foo) -> bool {
+    // CHECK: %[[R:.+]] = icmp ule i16 %[[A]], %[[B]]
+    // CHECK-NEXT: ret i1 %[[R]]
+    a <= b
+}
+
+// CHECK-LABEL: @check_gt
+// CHECK-SAME: (i16 %[[A:.+]], i16 %[[B:.+]])
+#[no_mangle]
+pub fn check_gt(a: Foo, b: Foo) -> bool {
+    // CHECK: %[[R:.+]] = icmp ugt i16 %[[A]], %[[B]]
+    // CHECK-NEXT: ret i1 %[[R]]
+    a > b
+}
+
+// CHECK-LABEL: @check_ge
+// CHECK-SAME: (i16 %[[A:.+]], i16 %[[B:.+]])
+#[no_mangle]
+pub fn check_ge(a: Foo, b: Foo) -> bool {
+    // CHECK: %[[R:.+]] = icmp uge i16 %[[A]], %[[B]]
+    // CHECK-NEXT: ret i1 %[[R]]
+    a >= b
+}