diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h
index 5fe2cff32..c0d362fa7 100644
--- a/Eigen/src/Core/arch/AVX/MathFunctions.h
+++ b/Eigen/src/Core/arch/AVX/MathFunctions.h
@@ -97,33 +97,36 @@ pexp<Packet4d>(const Packet4d& _x) {
 // For detail see here: http://www.beyond3d.com/content/articles/8/
 #if EIGEN_FAST_MATH
 template <>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
-psqrt<Packet8f>(const Packet8f& _x) {
-  Packet8f half = pmul(_x, pset1<Packet8f>(.5f));
-  Packet8f denormal_mask = _mm256_and_ps(
-      _mm256_cmp_ps(_x, pset1<Packet8f>((std::numeric_limits<float>::min)()),
-                    _CMP_LT_OQ),
-      _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_GE_OQ));
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet8f psqrt<Packet8f>(const Packet8f& _x) {
+  Packet8f minus_half_x = pmul(_x, pset1<Packet8f>(-0.5f));
+  Packet8f denormal_mask = pandnot(
+      pcmp_lt(_x, pset1<Packet8f>((std::numeric_limits<float>::min)())),
+      pcmp_lt(_x, pzero(_x)));
 
   // Compute approximate reciprocal sqrt.
   Packet8f x = _mm256_rsqrt_ps(_x);
   // Do a single step of Newton's iteration.
-  x = pmul(x, psub(pset1<Packet8f>(1.5f), pmul(half, pmul(x,x))));
+  x = pmul(x, pmadd(minus_half_x, pmul(x,x), pset1<Packet8f>(1.5f)));
   // Flush results for denormals to zero.
-  return _mm256_andnot_ps(denormal_mask, pmul(_x,x));
+  return pandnot(pmul(_x,x), denormal_mask);
 }
+
 #else
+
 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet8f psqrt<Packet8f>(const Packet8f& _x) {
   return _mm256_sqrt_ps(_x);
 }
+
 #endif
+
 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet4d psqrt<Packet4d>(const Packet4d& _x) {
   return _mm256_sqrt_pd(_x);
 }
-#if EIGEN_FAST_MATH
 
+#if EIGEN_FAST_MATH
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet8f prsqrt<Packet8f>(const Packet8f& _x) {
   _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000);
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index 5883eca38..14f3dbd0f 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -3273,26 +3273,26 @@ template<> EIGEN_STRONG_INLINE Packet4ui psqrt(const Packet4ui& a) {
 // effective latency. This is similar to Quake3's fast inverse square root.
 // For more details see: http://www.beyond3d.com/content/articles/8/
 template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& _x){
-  Packet4f half = vmulq_n_f32(_x, 0.5f);
+  Packet4f minus_half_x = vmulq_n_f32(_x, -0.5f);
   Packet4ui denormal_mask = vandq_u32(vcgeq_f32(_x, vdupq_n_f32(0.0f)),
                                       vcltq_f32(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())));
   // Compute approximate reciprocal sqrt.
   Packet4f x = vrsqrteq_f32(_x);
   // Do a single step of Newton's iteration.
   //the number 1.5f was set reference to Quake3's fast inverse square root
-  x = vmulq_f32(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x, x))));
+  x = pmul(x, pmadd(minus_half_x, pmul(x, x), pset1<Packet4f>(1.5f)));
   // Flush results for denormals to zero.
   return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(pmul(_x, x)), denormal_mask));
 }
 
-template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& _x){
-  Packet2f half = vmul_n_f32(_x, 0.5f);
+template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& _x) {
+  Packet2f minus_half_x = vmul_n_f32(_x, -0.5f);
   Packet2ui denormal_mask = vand_u32(vcge_f32(_x, vdup_n_f32(0.0f)),
                                      vclt_f32(_x, pset1<Packet2f>((std::numeric_limits<float>::min)())));
   // Compute approximate reciprocal sqrt.
   Packet2f x = vrsqrte_f32(_x);
   // Do a single step of Newton's iteration.
-  x = vmul_f32(x, psub(pset1<Packet2f>(1.5f), pmul(half, pmul(x, x))));
+  x = pmul(x, pmadd(minus_half_x, pmul(x, x), pset1<Packet2f>(1.5f)));
   // Flush results for denormals to zero.
   return vreinterpret_f32_u32(vbic_u32(vreinterpret_u32_f32(pmul(_x, x)), denormal_mask));
 }
@@ -3877,35 +3877,7 @@ template<> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Pack
 template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from)
 { return vreinterpretq_f64_u64(vdupq_n_u64(from)); }
 
-#if EIGEN_FAST_MATH
-
-// Functions for sqrt support packet2d.
-// The EIGEN_FAST_MATH version uses the vrsqrte_f64 approximation and one step
-// of Newton's method, at a cost of 1-2 bits of precision as opposed to the
-// exact solution. It does not handle +inf, or denormalized numbers correctly.
-// The main advantage of this approach is not just speed, but also the fact that
-// it can be inlined and pipelined with other computations, further reducing its
-// effective latency. This is similar to Quake3's fast inverse square root.
-// For more details see: http://www.beyond3d.com/content/articles/8/
-template<> EIGEN_STRONG_INLINE Packet2d psqrt(const Packet2d& _x){
-  Packet2d half = vmulq_n_f64(_x, 0.5);
-  Packet2ul denormal_mask = vandq_u64(vcgeq_f64(_x, vdupq_n_f64(0.0)),
-                                      vcltq_f64(_x, pset1<Packet2d>((std::numeric_limits<double>::min)())));
-  // Compute approximate reciprocal sqrt.
-  Packet2d x = vrsqrteq_f64(_x);
-  // Do a single step of Newton's iteration.
-  //the number 1.5f was set reference to Quake3's fast inverse square root
-  x = vmulq_f64(x, psub(pset1<Packet2d>(1.5), pmul(half, pmul(x, x))));
-  // Do two more Newton's iteration to get a result accurate to 1 ulp.
-  x = vmulq_f64(x, psub(pset1<Packet2d>(1.5), pmul(half, pmul(x, x))));
-  x = vmulq_f64(x, psub(pset1<Packet2d>(1.5), pmul(half, pmul(x, x))));
-  // Flush results for denormals to zero.
-  return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(pmul(_x, x)), denormal_mask));
-}
-
-#else
 template<> EIGEN_STRONG_INLINE Packet2d psqrt(const Packet2d& _x){ return vsqrtq_f64(_x); }
-#endif
 
 #endif // EIGEN_ARCH_ARM64
 
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h
index 2d7df2f7b..9f66d8ab3 100644
--- a/Eigen/src/Core/arch/SSE/MathFunctions.h
+++ b/Eigen/src/Core/arch/SSE/MathFunctions.h
@@ -86,17 +86,17 @@ Packet4f pcos<Packet4f>(const Packet4f& _x)
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet4f psqrt<Packet4f>(const Packet4f& _x)
 {
-  Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
-  Packet4f denormal_mask = _mm_and_ps(
-      _mm_cmpge_ps(_x, _mm_setzero_ps()),
-      _mm_cmplt_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())));
+  Packet4f minus_half_x = pmul(_x, pset1<Packet4f>(-0.5f));
+  Packet4f denormal_mask = pandnot(
+      pcmp_lt(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())),
+      pcmp_lt(_x, pzero(_x)));
 
   // Compute approximate reciprocal sqrt.
   Packet4f x = _mm_rsqrt_ps(_x);
   // Do a single step of Newton's iteration.
-  x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
+  x = pmul(x, pmadd(minus_half_x, pmul(x,x), pset1<Packet4f>(1.5f)));
   // Flush results for denormals to zero.
-  return _mm_andnot_ps(denormal_mask, pmul(_x,x));
+  return pandnot(pmul(_x,x), denormal_mask);
 }
 
 #else