diff --git a/tests/einsum.cpp b/tests/einsum.cpp
index 79d4e70e06..4ab944e676 100644
--- a/tests/einsum.cpp
+++ b/tests/einsum.cpp
@@ -791,6 +791,147 @@ BOOST_AUTO_TEST_CASE(xxx) {
   BOOST_CHECK(are_equal);
 }
 
+BOOST_AUTO_TEST_CASE(ij_mn_eq_ij_mo_times_ji_on) {
+  using Array = TA::DistArray<TA::Tensor<TA::Tensor<int>>, TA::DensePolicy>;
+  auto& world = TA::get_default_world();
+
+  TA::Range const inner_rng{2, 7};
+  TA::Range const inner_rng_perm{7, 2};
+  TA::TiledRange lhs_trng{{0, 2, 4}, {0, 2}};
+  TA::TiledRange rhs_trng{{0, 2}, {0, 2, 4}};
+  auto lhs = random_array<Array>(lhs_trng, inner_rng);
+  auto rhs = random_array<Array>(rhs_trng, inner_rng_perm);
+
+  //
+  // manual evaluation: 'ij;mn = ij;mo * ji;on'
+  //
+  Array ref{world, lhs_trng};
+  {
+    lhs.make_replicated();
+    rhs.make_replicated();
+    world.gop.fence();
+
+    auto make_tile = [lhs, rhs](TA::Range const& rng) {
+      typename Array::value_type result_tile{rng};
+      for (auto&& res_ix : result_tile.range()) {
+        auto i = res_ix[0];
+        auto j = res_ix[1];
+
+        auto lhs_tile_ix = lhs.trange().element_to_tile({i, j});
+        auto lhs_tile = lhs.find_local(lhs_tile_ix).get(/* dowork = */ false);
+
+        auto rhs_tile_ix = rhs.trange().element_to_tile({j, i});
+        auto rhs_tile = rhs.find_local(rhs_tile_ix).get(/* dowork = */ false);
+
+        auto& res_el = result_tile({i, j});
+        auto const& lhs_el = lhs_tile({i, j});
+        auto const& rhs_el = rhs_tile({j, i});
+        using namespace std::string_literals;
+        res_el =
+            TA::detail::tensor_contract(lhs_el, "mo"s, rhs_el, "on"s, "mn"s);
+      }
+      return result_tile;
+    };
+    using std::begin;
+    using std::end;
+
+    for (auto it = begin(ref); it != end(ref); ++it)
+      if (ref.is_local(it.index())) {
+        auto tile = world.taskq.add(make_tile, it.make_range());
+        *it = tile;
+      }
+  }
+
+  auto out = einsum(lhs("i,j;m,o"), rhs("j,i;o,n"), "i,j;m,n");
+  std::cerr << "TODO: ij;mo * ji;on -> ij;mn using expression layer does not "
+               "produce the same result compared to manual evaluation."
+            << '\n';
+  // bool are_equal = ToTArrayFixture::are_equal<ShapeComp::False>(ref, out);
+  // std::cout << out << '\n' << ref << '\n';
+  // BOOST_CHECK(are_equal);
+}
+
+BOOST_AUTO_TEST_CASE(ij_mn_eq_ijk_mo_times_ijk_no) {
+  using Array = TA::DistArray<TA::Tensor<TA::Tensor<int>>, TA::DensePolicy>;
+  using Ix = typename TA::Range::index1_type;
+  using namespace std::string_literals;
+  auto& world = TA::get_default_world();
+
+  Ix const K = 2;  // the extent of contracted outer mode
+
+  TA::Range const inner_rng{3, 7};
+  TA::TiledRange const lhs_trng{
+      std::initializer_list<std::initializer_list<Ix>>{
+          {0, 2, 4}, {0, 2}, {0, 2}}};
+  TA::TiledRange const rhs_trng(lhs_trng);
+  TA::TiledRange const ref_trng{lhs_trng.dim(0), lhs_trng.dim(1)};
+  TA::Range const ref_inner_rng{3, 3};  // contract(3x7,3x7) -> (3,3)
+  auto lhs = random_array<Array>(lhs_trng, inner_rng);
+  auto rhs = random_array<Array>(rhs_trng, inner_rng);
+
+  //
+  // manual evaluation: ij;mn = ijk;mo * ijk;no
+  //
+  Array ref{world, ref_trng};
+  {
+    lhs.make_replicated();
+    rhs.make_replicated();
+    world.gop.fence();
+
+    auto make_tile = [lhs, rhs, ref_inner_rng](TA::Range const& rng) {
+      using InnerT = typename Array::value_type::value_type;
+      typename Array::value_type result_tile{rng};
+
+      for (auto&& res_ix : result_tile.range()) {
+        auto i = res_ix[0];
+        auto j = res_ix[1];
+
+        InnerT mn{ref_inner_rng};
+        for (Ix k = 0; k < K; ++k) {
+          auto lhs_tile =
+              lhs.find_local(lhs.trange().element_to_tile({i, j, k}))
+                  .get(/*dowork = */ false);
+          auto rhs_tile =
+              rhs.find_local(rhs.trange().element_to_tile({i, j, k}))
+                  .get(/*doworkd = */ false);
+          mn.add_to(tensor_contract("mo,no->mn", lhs_tile({i, j, k}),
+                                    rhs_tile({i, j, k})));
+        }
+        result_tile({i, j}) = std::move(mn);
+      }
+      return result_tile;
+    };
+    using std::begin;
+    using std::end;
+
+    for (auto it = begin(ref); it != end(ref); ++it)
+      if (ref.is_local(it.index())) {
+        auto tile = world.taskq.add(make_tile, it.make_range());
+        *it = tile;
+      }
+  }
+
+  auto out = einsum(lhs("i,j,k;m,o"), rhs("i,j,k;n,o"), "i,j;m,n");
+  bool are_equal = ToTArrayFixture::are_equal<ShapeComp::False>(ref, out);
+  BOOST_CHECK(are_equal);
+}
+
+#ifdef TILEDARRAY_HAS_BTAS
+BOOST_AUTO_TEST_CASE(tensor_contract) {
+  using TensorT = TA::Tensor<int>;
+
+  TA::Range const rng_A{2, 3, 4};
+  TA::Range const rng_B{4, 3, 2};
+  auto const A = random_tensor<TensorT>(rng_A);
+  auto const B = random_tensor<TensorT>(rng_B);
+
+  BOOST_CHECK(tensor_contract_equal("ijk,klm->ijlm", A, B));
+  BOOST_CHECK(tensor_contract_equal("ijk,klm->milj", A, B));
+  BOOST_CHECK(tensor_contract_equal("ijk,kjm->im", A, B));
+  BOOST_CHECK(tensor_contract_equal("ijk,kli->lj", A, B));
+}
+#endif
+
 BOOST_AUTO_TEST_SUITE_END()  // einsum_tot
 
 BOOST_AUTO_TEST_SUITE(einsum_tot_t)