diff --git a/Project.toml b/Project.toml
index f3d7cdd2..ce73163a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "TensorOperations"
 uuid = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
 authors = ["Lukas Devos <lukas.devos@ugent.be>", "Maarten Van Damme <maartenvd1994@gmail.com>", "Jutho Haegeman <jutho.haegeman@ugent.be>"]
-version = "4.0.2"
+version = "4.0.3"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/implementation/strided.jl b/src/implementation/strided.jl
index 84046926..a63b149f 100644
--- a/src/implementation/strided.jl
+++ b/src/implementation/strided.jl
@@ -11,7 +11,24 @@ function tensoradd!(C::StridedView, pC::Index2Tuple,
     if !istrivialpermutation(pC) && Base.mightalias(C, A)
         throw(ArgumentError("output tensor must not be aliased with input tensor"))
     end
-    add!(C, permutedims(flag2op(conjA)(A), linearize(pC)), α, β)
+    A′ = permutedims(flag2op(conjA)(A), linearize(pC))
+    if isone(α)
+        if iszero(β)
+            return Strided._mapreducedim!(identity, +, zero, size(C), (C, A′))
+        elseif isone(β)
+            Strided._mapreducedim!(identity, +, nothing, size(C), (C, A′))
+        else
+            Strided._mapreducedim!(identity, +, y -> β * y, size(C), (C, A′))
+        end
+    else
+        if iszero(β)
+            Strided._mapreducedim!(x -> α * x, +, zero, size(C), (C, A′))
+        elseif isone(β)
+            Strided._mapreducedim!(x -> α * x, +, nothing, size(C), (C, A′))
+        else
+            Strided._mapreducedim!(x -> α * x, +, y -> β * y, size(C), (C, A′))
+        end
+    end
     return C
 end
 
@@ -29,22 +46,22 @@ function tensortrace!(C::StridedView, pC::Index2Tuple,
     tracesize = sizeA.(pA[1])
     newstrides = (strideA.(linearize(pC))..., (strideA.(pA[1]) .+ strideA.(pA[2]))...)
     newsize = (size(C)..., tracesize...)
-    A2 = flag2op(conjA)(StridedView(A.parent, newsize, newstrides, A.offset, A.op))
-    if α != 1
-        if β == 0
-            Strided._mapreducedim!(x -> α * x, +, zero, newsize, (C, A2))
-        elseif β == 1
-            Strided._mapreducedim!(x -> α * x, +, nothing, newsize, (C, A2))
+    A′ = flag2op(conjA)(StridedView(A.parent, newsize, newstrides, A.offset, A.op))
+    if isone(α)
+        if iszero(β)
+            return Strided._mapreducedim!(identity, +, zero, newsize, (C, A′))
+        elseif isone(β)
+            Strided._mapreducedim!(identity, +, nothing, newsize, (C, A′))
         else
-            Strided._mapreducedim!(x -> α * x, +, y -> β * y, newsize, (C, A2))
+            Strided._mapreducedim!(identity, +, y -> β * y, newsize, (C, A′))
         end
     else
-        if β == 0
-            return Strided._mapreducedim!(identity, +, zero, newsize, (C, A2))
-        elseif β == 1
-            Strided._mapreducedim!(identity, +, nothing, newsize, (C, A2))
+        if iszero(β)
+            Strided._mapreducedim!(x -> α * x, +, zero, newsize, (C, A′))
+        elseif isone(β)
+            Strided._mapreducedim!(x -> α * x, +, nothing, newsize, (C, A′))
         else
-            Strided._mapreducedim!(identity, +, y -> β * y, newsize, (C, A2))
+            Strided._mapreducedim!(x -> α * x, +, y -> β * y, newsize, (C, A′))
         end
     end
     return C
@@ -77,6 +94,30 @@ function tensorcontract!(C::StridedView{T}, pC::Index2Tuple,
     end
 end
 
+# reduce overhead for the case where it is just matrix multiplication
+function tensorcontract!(C::StridedView{T,2}, pC::Index2Tuple{1,1},
+                         A::StridedView{T,2}, pA::Index2Tuple{1,1}, conjA::Symbol,
+                         B::StridedView{T,2}, pB::Index2Tuple{1,1}, conjB::Symbol,
+                         α, β,
+                         backend::StridedBLAS=StridedBLAS()) where {T<:LinearAlgebra.BlasFloat}
+    argcheck_tensorcontract(C, pC, A, pA, B, pB)
+    dimcheck_tensorcontract(C, pC, A, pA, B, pB)
+
+    (Base.mightalias(C, A) || Base.mightalias(C, B)) &&
+        throw(ArgumentError("output tensor must not be aliased with input tensor"))
+
+    opA = flag2op(conjA)
+    opB = flag2op(conjB)
+    A′ = pA == ((1,), (2,)) ? opA(A) : opA(permutedims(A, (pA[1][1], pA[2][1])))
+    B′ = pB == ((1,), (2,)) ? opB(B) : opB(permutedims(B, (pB[1][1], pB[2][1])))
+    if pC == ((1,), (2,))
+        mul!(C, A′, B′, α, β)
+    elseif pC == ((2,), (1,))
+        mul!(C, transpose(A′), transpose(B′), α, β)
+    end
+    return C
+end
+
 function tensorcontract!(C::StridedView, pC::Index2Tuple,
                          A::StridedView, pA::Index2Tuple, conjA::Symbol,
                          B::StridedView, pB::Index2Tuple, conjB::Symbol,
@@ -177,7 +218,7 @@ function _unsafe_blas_contract!(C::StridedView{T}, ipC,
     return C
 end
 
-function makeblascontractable(A, pA, conjA, TC)
+@inline function makeblascontractable(A, pA, conjA, TC)
     flagA = isblascontractable(A, pA, conjA) && eltype(A) == TC
     if !flagA
         A_ = StridedView(TensorOperations.tensoralloc_add(TC, pA, A, conjA, true))
@@ -211,7 +252,7 @@ end
 
 _canfuse(::Dims{0}, ::Dims{0}) = true, 1, 1
 _canfuse(dims::Dims{1}, strides::Dims{1}) = true, dims[1], strides[1]
-function _canfuse(dims::Dims{N}, strides::Dims{N}) where {N}
+@inline function _canfuse(dims::Dims{N}, strides::Dims{N}) where {N}
     if dims[1] == 0
         return true, 0, 1
     elseif dims[1] == 1