diff --git a/stdlib/LinearAlgebra/src/diagonal.jl b/stdlib/LinearAlgebra/src/diagonal.jl
index 16528e6764531..dcaad4fdbdd91 100644
--- a/stdlib/LinearAlgebra/src/diagonal.jl
+++ b/stdlib/LinearAlgebra/src/diagonal.jl
@@ -442,16 +442,6 @@ function __muldiag_nonzeroalpha!(out, D::Diagonal, B::UpperOrLowerTriangular, _a
     end
     out
 end
-function __muldiag!(out, D::Diagonal, B, _add::MulAddMul)
-    require_one_based_indexing(out, B)
-    alpha, beta = _add.alpha, _add.beta
-    if iszero(alpha)
-        _rmul_or_fill!(out, beta)
-    else
-        __muldiag_nonzeroalpha!(out, D, B, _add)
-    end
-    return out
-end
 
 @inline function __muldiag_nonzeroalpha!(out, A, D::Diagonal, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
     beta = _add.beta
@@ -495,16 +485,6 @@ function __muldiag_nonzeroalpha!(out, A::UpperOrLowerTriangular, D::Diagonal, _a
     end
     out
 end
-function __muldiag!(out, A, D::Diagonal, _add::MulAddMul)
-    require_one_based_indexing(out, A)
-    alpha, beta = _add.alpha, _add.beta
-    if iszero(alpha)
-        _rmul_or_fill!(out, beta)
-    else
-        __muldiag_nonzeroalpha!(out, A, D, _add)
-    end
-    return out
-end
 
 @inline function __muldiag_nonzeroalpha!(out::Diagonal, D1::Diagonal, D2::Diagonal, _add::MulAddMul)
     d1 = D1.diag
@@ -515,15 +495,7 @@ end
     end
     out
 end
-function __muldiag!(out::Diagonal, D1::Diagonal, D2::Diagonal, _add::MulAddMul)
-    alpha, beta = _add.alpha, _add.beta
-    if iszero(alpha)
-        _rmul_or_fill!(out.diag, beta)
-    else
-        __muldiag_nonzeroalpha!(out, D1, D2, _add)
-    end
-    return out
-end
+
 @inline function __muldiag_nonzeroalpha!(out, D1::Diagonal, D2::Diagonal, _add::MulAddMul)
     d1 = D1.diag
     d2 = D2.diag
@@ -532,11 +504,26 @@ end
     end
     out
 end
+
+# muldiag mainly handles the zero-alpha case, so that we need only 
+# specialize the non-trivial case
+function __muldiag!(out, A, B, _add::MulAddMul)
+    require_one_based_indexing(out, A, B)
+    alpha, beta = _add.alpha, _add.beta
+    if iszero(alpha)
+        _rmul_or_fill!(out, beta)
+    else
+        __muldiag_nonzeroalpha!(out, A, B, _add)
+    end
+    return out
+end
+
 function __muldiag!(out, D1::Diagonal, D2::Diagonal, _add::MulAddMul{ais1}) where {ais1}
     require_one_based_indexing(out)
     alpha, beta = _add.alpha, _add.beta
     _rmul_or_fill!(out, beta)
     if !iszero(alpha)
+        # we ony update the diagonal
         _add_bis1 = MulAddMul{ais1,false,typeof(alpha),Bool}(alpha,true)
         __muldiag_nonzeroalpha!(out, D1, D2, _add_bis1)
     end