diff --git a/compiler/rustc_codegen_cranelift/src/intrinsics/mod.rs b/compiler/rustc_codegen_cranelift/src/intrinsics/mod.rs
index 584e4a895be9b..97f88e5fbfec3 100644
--- a/compiler/rustc_codegen_cranelift/src/intrinsics/mod.rs
+++ b/compiler/rustc_codegen_cranelift/src/intrinsics/mod.rs
@@ -409,6 +409,9 @@ fn codegen_float_intrinsic_call<'tcx>(
         sym::sinf64 => ("sin", 1, fx.tcx.types.f64, types::F64),
         sym::sinf128 => ("sinf128", 1, fx.tcx.types.f128, types::F128),
 
+        sym::tanhf32 => ("tanhf", 1, fx.tcx.types.f32, types::F32),
+        sym::tanhf64 => ("tanh", 1, fx.tcx.types.f64, types::F64),
+
         sym::cosf16 => return false, // has a fallback via f32
         sym::cosf32 => ("cosf", 1, fx.tcx.types.f32, types::F32),
         sym::cosf64 => ("cos", 1, fx.tcx.types.f64, types::F64),
diff --git a/compiler/rustc_codegen_gcc/src/intrinsic/mod.rs b/compiler/rustc_codegen_gcc/src/intrinsic/mod.rs
index b3b1bea68e0b4..7b67b1d03754b 100644
--- a/compiler/rustc_codegen_gcc/src/intrinsic/mod.rs
+++ b/compiler/rustc_codegen_gcc/src/intrinsic/mod.rs
@@ -64,6 +64,8 @@ fn get_simple_intrinsic<'gcc, 'tcx>(
         sym::powif64 => "__builtin_powi",
         sym::sinf32 => "sinf",
         sym::sinf64 => "sin",
+        sym::tanhf32 => "tanhf",
+        sym::tanhf64 => "tanh",
         sym::cosf32 => "cosf",
         sym::cosf64 => "cos",
         sym::powf32 => "powf",
diff --git a/compiler/rustc_codegen_llvm/src/intrinsic.rs b/compiler/rustc_codegen_llvm/src/intrinsic.rs
index 36709e4ff954f..8a4b7bb30da8c 100644
--- a/compiler/rustc_codegen_llvm/src/intrinsic.rs
+++ b/compiler/rustc_codegen_llvm/src/intrinsic.rs
@@ -71,6 +71,9 @@ fn call_simple_intrinsic<'ll, 'tcx>(
         sym::sinf64 => ("llvm.sin", &[bx.type_f64()]),
         sym::sinf128 => ("llvm.sin", &[bx.type_f128()]),
 
+        sym::tanhf32 => ("llvm.tanh", &[bx.type_f32()]),
+        sym::tanhf64 => ("llvm.tanh", &[bx.type_f64()]),
+
         sym::cosf16 => ("llvm.cos", &[bx.type_f16()]),
         sym::cosf32 => ("llvm.cos", &[bx.type_f32()]),
         sym::cosf64 => ("llvm.cos", &[bx.type_f64()]),
diff --git a/compiler/rustc_codegen_llvm/src/lib.rs b/compiler/rustc_codegen_llvm/src/lib.rs
index a8a8edf98bd86..e308e76f5a33d 100644
--- a/compiler/rustc_codegen_llvm/src/lib.rs
+++ b/compiler/rustc_codegen_llvm/src/lib.rs
@@ -337,6 +337,7 @@ impl CodegenBackend for LlvmCodegenBackend {
             sym::integer_min,
 
             // Fallback via libm, but the LLVM intrinsic is used instead.
+            sym::tanhf32, sym::tanhf64,
             sym::sinf16, sym::sinf32, sym::sinf64,
             sym::cosf16, sym::cosf32, sym::cosf64,
             sym::powf16, sym::powf32, sym::powf64,
diff --git a/compiler/rustc_hir_analysis/src/check/intrinsic.rs b/compiler/rustc_hir_analysis/src/check/intrinsic.rs
index 3354b1e4bc3e4..987d8fe93ccd3 100644
--- a/compiler/rustc_hir_analysis/src/check/intrinsic.rs
+++ b/compiler/rustc_hir_analysis/src/check/intrinsic.rs
@@ -214,6 +214,8 @@ fn intrinsic_operation_unsafety(tcx: TyCtxt<'_>, intrinsic_id: LocalDefId) -> hi
         | sym::sqrtf64
         | sym::sqrtf128
         | sym::sub_with_overflow
+        | sym::tanhf32
+        | sym::tanhf64
         | sym::three_way_compare
         | sym::truncf16
         | sym::truncf32
@@ -446,6 +448,9 @@ pub(crate) fn check_intrinsic_type(
         sym::sinf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
         sym::sinf128 => (0, 0, vec![tcx.types.f128], tcx.types.f128),
 
+        sym::tanhf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
+        sym::tanhf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
+
         sym::cosf16 => (0, 0, vec![tcx.types.f16], tcx.types.f16),
         sym::cosf32 => (0, 0, vec![tcx.types.f32], tcx.types.f32),
         sym::cosf64 => (0, 0, vec![tcx.types.f64], tcx.types.f64),
diff --git a/compiler/rustc_span/src/symbol.rs b/compiler/rustc_span/src/symbol.rs
index 057ea6bd3d0a2..1d68da8a23cd7 100644
--- a/compiler/rustc_span/src/symbol.rs
+++ b/compiler/rustc_span/src/symbol.rs
@@ -2099,6 +2099,8 @@ symbols! {
         sync,
         synthetic,
         t32,
+        tanhf32,
+        tanhf64,
         target,
         target_abi,
         target_arch,
diff --git a/library/core/src/intrinsics/mod.rs b/library/core/src/intrinsics/mod.rs
index 4e9187f7933b2..69c4109ea50c2 100644
--- a/library/core/src/intrinsics/mod.rs
+++ b/library/core/src/intrinsics/mod.rs
@@ -1143,6 +1143,19 @@ pub fn sinf32(x: f32) -> f32 {
 pub fn sinf64(x: f64) -> f64 {
     libm::likely_available::sin(x)
 }
+#[inline]
+#[rustc_intrinsic]
+#[rustc_nounwind]
+pub fn tanhf64(x: f64) -> f64 {
+    libm::likely_available::tanh(x)
+}
+#[inline]
+#[rustc_intrinsic]
+#[rustc_nounwind]
+pub fn tanhf32(x: f32) -> f32 {
+    libm::likely_available::tanhf(x)
+}
+
 /// Returns the sine of an `f128`.
 ///
 /// The stabilized version of this intrinsic is
diff --git a/library/std/src/num/f32.rs b/library/std/src/num/f32.rs
index 385533748cb5d..e8fb94d988910 100644
--- a/library/std/src/num/f32.rs
+++ b/library/std/src/num/f32.rs
@@ -1047,8 +1047,6 @@ impl f32 {
     ///
     /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
     /// can even differ within the same execution from one invocation to the next.
-    /// This function currently corresponds to the `tanhf` from libc on Unix
-    /// and Windows. Note that this might change in the future.
     ///
     /// # Examples
     ///
@@ -1068,7 +1066,7 @@ impl f32 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn tanh(self) -> f32 {
-        cmath::tanhf(self)
+        intrinsics::tanhf32(self)
     }
 
     /// Inverse hyperbolic sine function.
diff --git a/library/std/src/num/f64.rs b/library/std/src/num/f64.rs
index 66482a8b654a5..6132efea30bdf 100644
--- a/library/std/src/num/f64.rs
+++ b/library/std/src/num/f64.rs
@@ -1047,8 +1047,6 @@ impl f64 {
     ///
     /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
     /// can even differ within the same execution from one invocation to the next.
-    /// This function currently corresponds to the `tanh` from libc on Unix
-    /// and Windows. Note that this might change in the future.
     ///
     /// # Examples
     ///
@@ -1068,7 +1066,7 @@ impl f64 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn tanh(self) -> f64 {
-        cmath::tanh(self)
+       intrinsics::tanhf64(self)
     }
 
     /// Inverse hyperbolic sine function.
diff --git a/library/std/src/sys/cmath.rs b/library/std/src/sys/cmath.rs
index 2104087141d1a..5254990848d9e 100644
--- a/library/std/src/sys/cmath.rs
+++ b/library/std/src/sys/cmath.rs
@@ -20,7 +20,6 @@ unsafe extern "C" {
     pub safe fn log1pf(n: f32) -> f32;
     pub safe fn sinh(n: f64) -> f64;
     pub safe fn tan(n: f64) -> f64;
-    pub safe fn tanh(n: f64) -> f64;
     pub safe fn tgamma(n: f64) -> f64;
     pub safe fn tgammaf(n: f32) -> f32;
     pub safe fn lgamma_r(n: f64, s: &mut i32) -> f64;
diff --git a/tests/codegen-llvm/intrinsics/tanh.rs b/tests/codegen-llvm/intrinsics/tanh.rs
new file mode 100644
index 0000000000000..f9552d8567fee
--- /dev/null
+++ b/tests/codegen-llvm/intrinsics/tanh.rs
@@ -0,0 +1,48 @@
+//@ revisions: DEV OPT
+//@ [DEV] compile-flags: -C no-prepopulate-passes
+//@ [OPT] compile-flags: -O
+
+// We previously lowered tanh to libm calls, which would set errno and thus prevent a couple of
+// optimizations, since LLVM would mark the call as `memory(errnomem: write)`.
+// LLVM since gained additional math intrinsics, including tanh, to which we're now lowering
+// instead. They are marked as `readnone`, and thus allow the optimizations shown below.
+
+#![crate_type = "lib"]
+
+// CHECK-LABEL: @tanhf64
+#[no_mangle]
+pub fn tanhf64(x: f64) -> f64 {
+    // CHECK: call double @llvm.tanh.f64
+    // CHECK-NOT: call double @tanh(
+    x.tanh()
+}
+
+// CHECK-LABEL: @tanhf32
+#[no_mangle]
+pub fn tanhf32(x: f32) -> f32 {
+    // CHECK: call float @llvm.tanh.f32
+    // CHECK-NOT: call float @tanhf(
+    x.tanh()
+}
+
+// Since we're now marked as readnone, the call to tanh can be optimized away
+// CHECK-LABEL: @dce_tanh
+#[no_mangle]
+pub fn dce_tanh(x: f64) -> f64 {
+    // DEV: call double @llvm.tanh.f64
+    // OPT-NOT: llvm.tanh
+    let _ = x.tanh();
+    1.0
+}
+
+// Since we're now marked as speculate, we can fold the branch into a select
+// CHECK-LABEL: @speculate
+#[no_mangle]
+pub fn speculate(x: f64, cond: bool) -> f64 {
+    // DEV: br i1 %cond
+    // OPT-NOT: br i1
+    // OPT: %0 = tail call double @llvm.tanh.f64(double %x)
+    // OPT-NEXT: %_0.sroa.0.0 = select i1 %cond, double %0, double 0.000000e+00
+    // OPT-NEXT: ret double %_0.sroa.0.0
+    if cond { x.tanh() } else { 0.0 }
+}