diff --git a/taco/iter-spaces.cpp b/taco/iter-spaces.cpp
new file mode 100644
index 0000000..2f5443c
--- /dev/null
+++ b/taco/iter-spaces.cpp
@@ -0,0 +1,76 @@
+#include "bench.h"
+#include "benchmark/benchmark.h"
+
+#include "taco/tensor.h"
+#include "taco/index_notation/tensor_operator.h"
+
+using namespace taco;
+
+struct NoOp {
+  ir::Expr operator()(const std::vector<ir::Expr>& v) {
+    return 1;
+  }
+};
+
+struct UnionAlgebra {
+  IterationAlgebra operator()(const std::vector<IndexExpr>& regions) {
+    return Union(regions[0], regions[1]);
+  }
+};
+
+struct IntersectAlgebra {
+  IterationAlgebra operator()(const std::vector<IndexExpr>& regions) {
+    return Intersect(regions[0], regions[1]);
+  }
+};
+
+struct AMinusBAlgebra {
+  IterationAlgebra operator()(const std::vector<IndexExpr>& regions) {
+    auto nointersect = Complement(Intersect(regions[0], regions[1]));
+    return Intersect(regions[0], nointersect);
+  }
+};
+
+struct AAlgebra {
+  IterationAlgebra operator()(const std::vector<IndexExpr>& regions) {
+    return Union(regions[0], Intersect(regions[0], regions[1]));
+  }
+};
+
+struct XorAlgebra {
+  IterationAlgebra operator()(const std::vector<IndexExpr>& regions) {
+    IterationAlgebra noIntersect = Complement(Intersect(regions[0], regions[1]));
+    return Intersect(noIntersect, Union(regions[0], regions[1]));
+  }
+};
+
+Func unionOp("union", NoOp(), UnionAlgebra());
+Func intersectOp("intersect", NoOp(), IntersectAlgebra());
+Func aMinusB("aMinusB", NoOp(), AMinusBAlgebra());
+Func aBIntersectOp("aBIntersect", NoOp(), AAlgebra());
+Func aubminusanb("xor", NoOp(), XorAlgebra());
+static void bench_iteration_spaces(benchmark::State& state, Func op) {
+  int dim = state.range(0);
+  auto sparsity = 0.01;
+  auto f = CSR;
+  Tensor<double> matrix = loadRandomTensor("A", {dim, dim}, sparsity, f);
+  Tensor<double> matrix1 = loadRandomTensor("B", {dim, dim}, sparsity, f, 1 /* variant */);
+
+  for (auto _ : state) {
+    state.PauseTiming();
+    Tensor<double> result("result", {dim, dim}, f);
+    IndexVar i("i"), j("j");
+    result(i, j) = op(matrix(i, j), matrix1(i, j));
+    // result.setAssembleWhileCompute(true);
+    result.compile();
+    std::cout << result.getSource() << std::endl;
+    state.ResumeTiming();
+    // result.compute();
+  }
+}
+std::vector<std::vector<int64_t>> sizes = {{1000, 2500, 5000, 10000, 20000, 40000}};
+TACO_BENCH_ARGS(bench_iteration_spaces, aub, unionOp)->ArgsProduct(sizes);
+TACO_BENCH_ARGS(bench_iteration_spaces, anb, intersectOp)->ArgsProduct(sizes);
+TACO_BENCH_ARGS(bench_iteration_spaces, a-b, aMinusB)->ArgsProduct(sizes);
+TACO_BENCH_ARGS(bench_iteration_spaces, auanb, aBIntersectOp)->ArgsProduct(sizes);
+TACO_BENCH_ARGS(bench_iteration_spaces, aub-anb, aubminusanb)->ArgsProduct(sizes);