diff --git a/include/xsimd/arch/xsimd_avx.hpp b/include/xsimd/arch/xsimd_avx.hpp
index a5fa3266d..7a2436d5a 100644
--- a/include/xsimd/arch/xsimd_avx.hpp
+++ b/include/xsimd/arch/xsimd_avx.hpp
@@ -1064,22 +1064,10 @@ namespace xsimd
             tmp = _mm256_hadd_ps(tmp, tmp);
             return _mm_cvtss_f32(_mm256_extractf128_ps(tmp, 0));
         }
-        template <class A>
-        XSIMD_INLINE double reduce_add(batch<double, A> const& rhs, requires_arch<avx>) noexcept
-        {
-            // rhs = (x0, x1, x2, x3)
-            // tmp = (x2, x3, x0, x1)
-            __m256d tmp = _mm256_permute2f128_pd(rhs, rhs, 1);
-            // tmp = (x2+x0, x3+x1, -, -)
-            tmp = _mm256_add_pd(rhs, tmp);
-            // tmp = (x2+x0+x3+x1, -, -, -)
-            tmp = _mm256_hadd_pd(tmp, tmp);
-            return _mm_cvtsd_f64(_mm256_extractf128_pd(tmp, 0));
-        }
-        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
+        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value || std::is_same<T, double>::value, void>::type>
         XSIMD_INLINE T reduce_add(batch<T, A> const& self, requires_arch<avx>) noexcept
         {
-            __m128i low, high;
+            typename batch<T, sse4_2>::register_type low, high;
             detail::split_avx(self, low, high);
             batch<T, sse4_2> blow(low), bhigh(high);
             return reduce_add(blow) + reduce_add(bhigh);
diff --git a/include/xsimd/arch/xsimd_avx512f.hpp b/include/xsimd/arch/xsimd_avx512f.hpp
index 79e29b7b0..d58724a61 100644
--- a/include/xsimd/arch/xsimd_avx512f.hpp
+++ b/include/xsimd/arch/xsimd_avx512f.hpp
@@ -1506,22 +1506,12 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE float reduce_add(batch<float, A> const& rhs, requires_arch<avx512f>) noexcept
         {
-            __m128 tmp1 = _mm512_extractf32x4_ps(rhs, 0);
-            __m128 tmp2 = _mm512_extractf32x4_ps(rhs, 1);
-            __m128 tmp3 = _mm512_extractf32x4_ps(rhs, 2);
-            __m128 tmp4 = _mm512_extractf32x4_ps(rhs, 3);
-            __m128 res1 = _mm_add_ps(tmp1, tmp2);
-            __m128 res2 = _mm_add_ps(tmp3, tmp4);
-            __m128 res3 = _mm_add_ps(res1, res2);
-            return reduce_add(batch<float, sse4_2>(res3), sse4_2 {});
+            return _mm512_reduce_add_ps(rhs);
         }
         template <class A>
         XSIMD_INLINE double reduce_add(batch<double, A> const& rhs, requires_arch<avx512f>) noexcept
         {
-            __m256d tmp1 = _mm512_extractf64x4_pd(rhs, 1);
-            __m256d tmp2 = _mm512_extractf64x4_pd(rhs, 0);
-            __m256d res1 = _mm256_add_pd(tmp1, tmp2);
-            return reduce_add(batch<double, avx2>(res1), avx2 {});
+            return _mm512_reduce_add_pd(rhs);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE T reduce_add(batch<T, A> const& self, requires_arch<avx512f>) noexcept
diff --git a/include/xsimd/arch/xsimd_sse3.hpp b/include/xsimd/arch/xsimd_sse3.hpp
index ffdc5bc9f..9dbc4b343 100644
--- a/include/xsimd/arch/xsimd_sse3.hpp
+++ b/include/xsimd/arch/xsimd_sse3.hpp
@@ -50,12 +50,6 @@ namespace xsimd
             __m128 tmp1 = _mm_hadd_ps(tmp0, tmp0);
             return _mm_cvtss_f32(tmp1);
         }
-        template <class A>
-        XSIMD_INLINE double reduce_add(batch<double, A> const& self, requires_arch<sse3>) noexcept
-        {
-            __m128d tmp0 = _mm_hadd_pd(self, self);
-            return _mm_cvtsd_f64(tmp0);
-        }
 
     }