diff --git a/libc/src/__support/FPUtil/PolyEval.h b/libc/src/__support/FPUtil/PolyEval.h
--- a/libc/src/__support/FPUtil/PolyEval.h
+++ b/libc/src/__support/FPUtil/PolyEval.h
@@ -35,6 +35,12 @@
 } // namespace fputil
 } // namespace __llvm_libc
 
+#ifdef LLVM_LIBC_ARCH_X86_64
+
+#include "x86_64/PolyEval.h"
+
+#endif // LLVM_LIBC_ARCH_X86_64
+
 #else
 
 namespace __llvm_libc {
diff --git a/libc/src/__support/FPUtil/x86_64/FMA.h b/libc/src/__support/FPUtil/x86_64/FMA.h
--- a/libc/src/__support/FPUtil/x86_64/FMA.h
+++ b/libc/src/__support/FPUtil/x86_64/FMA.h
@@ -16,27 +16,34 @@
 #endif
 
 #include "src/__support/CPP/TypeTraits.h"
+#include <immintrin.h>
 
 namespace __llvm_libc {
 namespace fputil {
 
 template <typename T>
-static inline cpp::EnableIfType<cpp::IsSame<T, float>::Value, T> fma(T x, T y,
-                                                                     T z) {
-  float result = x;
-  __asm__ __volatile__("vfmadd213ss %x2, %x1, %x0"
-                       : "+x"(result)
-                       : "x"(y), "x"(z));
+__attribute__((target(
+    "fma"))) static inline cpp::EnableIfType<cpp::IsSame<T, float>::Value, T>
+fma(T x, T y, T z) {
+  float result;
+  __m128 xmm = _mm_load_ss(&x);
+  __m128 ymm = _mm_load_ss(&y);
+  __m128 zmm = _mm_load_ss(&z);
+  __m128 r = _mm_fmadd_ss(xmm, ymm, zmm);
+  _mm_store_ss(&result, r);
   return result;
 }
 
 template <typename T>
-static inline cpp::EnableIfType<cpp::IsSame<T, double>::Value, T> fma(T x, T y,
-                                                                      T z) {
-  double result = x;
-  __asm__ __volatile__("vfmadd213sd %x2, %x1, %x0"
-                       : "+x"(result)
-                       : "x"(y), "x"(z));
+__attribute__((target(
+    "fma"))) static inline cpp::EnableIfType<cpp::IsSame<T, double>::Value, T>
+fma(T x, T y, T z) {
+  double result;
+  __m128d xmm = _mm_load_sd(&x);
+  __m128d ymm = _mm_load_sd(&y);
+  __m128d zmm = _mm_load_sd(&z);
+  __m128d r = _mm_fmadd_sd(xmm, ymm, zmm);
+  _mm_store_sd(&result, r);
   return result;
 }
 
diff --git a/libc/src/__support/FPUtil/x86_64/PolyEval.h b/libc/src/__support/FPUtil/x86_64/PolyEval.h
new file mode 100644
--- /dev/null
+++ b/libc/src/__support/FPUtil/x86_64/PolyEval.h
@@ -0,0 +1,86 @@
+//===-- Optimized PolyEval implementations for x86_64 --------- C++ -----*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_SUPPORT_FPUTIL_X86_64_POLYEVAL_H
+#define LLVM_LIBC_SRC_SUPPORT_FPUTIL_X86_64_POLYEVAL_H
+
+#include "src/__support/architectures.h"
+
+#if !defined(LLVM_LIBC_ARCH_X86_64)
+#error "Invalid include"
+#endif
+
+#include <immintrin.h>
+
+namespace __llvm_libc {
+namespace fputil {
+
+// Cubic polynomials:
+//   polyeval(x, a0, a1, a2, a3) = a3*x^3 + a2*x^2 + a1*x + a0
+template <>
+__attribute__((target("fma"))) inline float
+polyeval(float x, float a0, float a1, float a2, float a3) {
+  __m128 xmm = _mm_set1_ps(x);
+  __m128 a13 = _mm_set_ps(0.0f, x, a3, a1);
+  __m128 a02 = _mm_set_ps(0.0f, 0.0f, a2, a0);
+  // r = (0, x^2, a3*x + a2, a1*x + a0)
+  __m128 r = _mm_fmadd_ps(a13, xmm, a02);
+  // result = (a3*x + a2) * x^2 + (a1*x + a0)
+  return fma(r[2], r[1], r[0]);
+}
+
+template <>
+__attribute__((target("fma"))) inline double
+polyeval(double x, double a0, double a1, double a2, double a3) {
+  __m256d xmm = _mm256_set1_pd(x);
+  __m256d a13 = _mm256_set_pd(0.0, x, a3, a1);
+  __m256d a02 = _mm256_set_pd(0.0, 0.0, a2, a0);
+  // r = (0, x^2, a3*x + a2, a1*x + a0)
+  __m256d r = _mm256_fmadd_pd(a13, xmm, a02);
+  // result = (a3*x + a2) * x^2 + (a1*x + a0)
+  return fma(r[2], r[1], r[0]);
+}
+
+// Quintic polynomials:
+//   polyeval(x, a0, a1, a2, a3, a4, a5) = a5*x^5 + a4*x^4 + a3*x^3 + a2*x^2 +
+//                                         + a1*x + a0
+template <>
+__attribute__((target("fma"))) inline float
+polyeval(float x, float a0, float a1, float a2, float a3, float a4, float a5) {
+  __m128 xmm = _mm_set1_ps(x);
+  __m128 a25 = _mm_set_ps(0.0f, x, a5, a2);
+  __m128 a14 = _mm_set_ps(0.0f, 0.0f, a4, a1);
+  __m128 a03 = _mm_set_ps(0.0f, 0.0f, a3, a0);
+  // r1 = (0, x^2, a5*x + a4, a2*x + a1)
+  __m128 r1 = _mm_fmadd_ps(a25, xmm, a14);
+  // r2 = (0, x^3, (a5*x + a4)*x + a3, (a2*x + a1)*x + a0
+  __m128 r2 = _mm_fmadd_ps(r1, xmm, a03);
+  // result = ((a5*x + a4)*x + a3) * x^3 + ((a2*x + a1)*x + a0)
+  return fma(r2[2], r2[1], r2[0]);
+}
+
+template <>
+__attribute__((target("fma"))) inline double
+polyeval(double x, double a0, double a1, double a2, double a3, double a4,
+         double a5) {
+  __m256d xmm = _mm256_set1_pd(x);
+  __m256d a25 = _mm256_set_pd(0.0, x, a5, a2);
+  __m256d a14 = _mm256_set_pd(0.0, 0.0, a4, a1);
+  __m256d a03 = _mm256_set_pd(0.0, 0.0, a3, a0);
+  // r1 = (0, x^2, a5*x + a4, a2*x + a1)
+  __m256d r1 = _mm256_fmadd_pd(a25, xmm, a14);
+  // r2 = (0, x^3, (a5*x + a4)*x + a3, (a2*x + a1)*x + a0
+  __m256d r2 = _mm256_fmadd_pd(r1, xmm, a03);
+  // result = ((a5*x + a4)*x + a3) * x^3 + ((a2*x + a1)*x + a0)
+  return fma(r2[2], r2[1], r2[0]);
+}
+
+} // namespace fputil
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_SUPPORT_FPUTIL_X86_64_POLYEVAL_H
diff --git a/libc/test/src/math/expm1f_test.cpp b/libc/test/src/math/expm1f_test.cpp
--- a/libc/test/src/math/expm1f_test.cpp
+++ b/libc/test/src/math/expm1f_test.cpp
@@ -108,6 +108,6 @@
     // wider precision.
     if (isnan(result) || isinf(result) || errno != 0)
       continue;
-    ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 1.5);
+    ASSERT_MPFR_MATCH(mpfr::Operation::Expm1, x, __llvm_libc::expm1f(x), 2.2);
   }
 }