diff --git a/ADOL-C/boost-test/uni5_for.cpp b/ADOL-C/boost-test/uni5_for.cpp
index 9129fd74..1d98f63f 100644
--- a/ADOL-C/boost-test/uni5_for.cpp
+++ b/ADOL-C/boost-test/uni5_for.cpp
@@ -242,4 +242,165 @@ BOOST_AUTO_TEST_CASE(FmaxOperator_HOV_Forward) {
   myfree3(X);
   myfree3(Y);
 }
+
+BOOST_AUTO_TEST_CASE(FminOperator_HOV_Forward) {
+  const int16_t tag = 0;
+  const size_t dim_out = 1;
+  const size_t dim_in = 2;
+  const size_t degree = 2;
+  const size_t num_dirs = 3;
+  std::vector<double> in{4.0, 3.2};
+  std::vector<adouble> indep(dim_in);
+  std::vector<double> out(dim_out);
+
+  trace_on(tag);
+  std::for_each(in.begin(), in.end(), [&, i = 0](int value) mutable {
+    indep[i] <<= in[i];
+    i++;
+  });
+
+  // max(x^2, y^3)
+  adouble dep = fmin(-pow(indep[0], 2), -pow(indep[1], 3));
+
+  dep >>= out[0];
+  trace_off();
+
+  double ***X = myalloc3(dim_in, num_dirs, degree);
+  double ***Y = myalloc3(dim_out, num_dirs, degree);
+
+  X[0][0][0] = 1.0;
+  X[1][0][0] = 1.9;
+
+  X[0][1][0] = 2.0;
+  X[1][1][0] = 3.0;
+
+  X[0][2][0] = 1.0;
+  X[1][2][0] = -1.0;
+
+  X[0][0][1] = -1.0;
+  X[1][0][1] = 1.0;
+
+  X[0][1][1] = -2.0;
+  X[1][1][1] = -3.0;
+
+  X[0][2][1] = -1.0;
+  X[1][2][1] = 1.0;
+
+  /****************************
+  TEST A < B
+  *****************************/
+  std::vector<double> test_in{4.0, 3.2};
+  // max(x^2, y^3)
+  double test_out =
+      std::fmin(-std::pow(test_in[0], 2), -std::pow(test_in[1], 3));
+
+  hov_forward(tag, dim_out, dim_in, degree, num_dirs, test_in.data(), X,
+              out.data(), Y);
+
+  BOOST_TEST(out[0] == test_out, tt::tolerance(tol));
+  BOOST_TEST(Y[0][0][0] == -3 * std::pow(test_in[1], 2) * X[1][0][0],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][1][0] == -3 * std::pow(test_in[1], 2) * X[1][1][0],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][2][0] == -3 * std::pow(test_in[1], 2) * X[1][2][0],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][0][1] ==
+                 -1.0 / 2.0 * 6.0 * test_in[1] * X[1][0][0] * X[1][0][0] -
+                     3.0 * std::pow(test_in[1], 2.0) * X[1][0][1],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][1][1] ==
+                 -1.0 / 2.0 * 6.0 * test_in[1] * X[1][1][0] * X[1][1][0] -
+                     3.0 * std::pow(test_in[1], 2.0) * X[1][1][1],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][2][1] ==
+                 -1.0 / 2.0 * 6.0 * test_in[1] * X[1][2][0] * X[1][2][0] -
+                     3.0 * std::pow(test_in[1], 2.0) * X[1][2][1],
+             tt::tolerance(tol));
+
+  /**************************
+  TEST A > B
+  ***************************/
+
+  // test_in[0] = 4.0
+  test_in[1] = 1.0;
+  // max(x^2, y^3)
+  test_out = std::fmin(-std::pow(test_in[0], 2), -std::pow(test_in[1], 3));
+  hov_forward(tag, dim_out, dim_in, degree, num_dirs, test_in.data(), X,
+              out.data(), Y);
+
+  BOOST_TEST(out[0] == test_out, tt::tolerance(tol));
+  BOOST_TEST(Y[0][0][0] == -2 * test_in[0] * X[0][0][0], tt::tolerance(tol));
+  BOOST_TEST(Y[0][1][0] == -2 * test_in[0] * X[0][1][0], tt::tolerance(tol));
+  BOOST_TEST(Y[0][2][0] == -2 * test_in[0] * X[0][2][0], tt::tolerance(tol));
+  BOOST_TEST(Y[0][0][1] == -1.0 / 2.0 * 2.0 * X[0][0][0] * X[0][0][0] -
+                               2.0 * test_in[0] * X[0][0][1],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][1][1] == -1.0 / 2.0 * 2.0 * X[0][1][0] * X[0][1][0] -
+                               2.0 * test_in[0] * X[0][1][1],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][2][1] == -1.0 / 2.0 * 2.0 * X[0][2][0] * X[0][2][0] -
+                               2.0 * test_in[0] * X[0][2][1],
+             tt::tolerance(tol));
+
+  /**************************
+    TEST A == B
+  ***************************/
+
+  test_in[0] = 1.0;
+  test_in[1] = 1.0;
+
+  // max(x^2, y^3)
+  test_out = std::fmin(-std::pow(test_in[0], 2), -std::pow(test_in[1], 3));
+
+  // A < B
+  X[0][0][0] = 1.0;
+  X[1][0][0] = 1.9;
+
+  // A > B
+  X[0][1][0] = 3.0;
+  X[1][1][0] = 2.0;
+
+  // A == B
+  X[0][2][0] = 1.0;
+  X[1][2][0] = 1.0;
+
+  X[0][0][1] = -1.0;
+  X[1][0][1] = 1.0;
+
+  X[0][1][1] = -2.0;
+  X[1][1][1] = -3.0;
+
+  // A < B
+  X[0][2][1] = 1.0;
+  X[1][2][1] = 2.0;
+
+  hov_forward(tag, dim_out, dim_in, degree, num_dirs, test_in.data(), X,
+              out.data(), Y);
+  BOOST_TEST(out[0] == test_out, tt::tolerance(tol));
+
+  // A < B
+  BOOST_TEST(Y[0][0][0] == -3 * std::pow(test_in[1], 2) * X[1][0][0],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][0][1] ==
+                 -1.0 / 2.0 * 6.0 * test_in[1] * X[1][0][0] * X[1][0][0] -
+                     3.0 * std::pow(test_in[1], 2.0) * X[1][0][1],
+             tt::tolerance(tol));
+
+  // A < B
+  BOOST_TEST(Y[0][1][0] == -2 * test_in[0] * X[0][1][0], tt::tolerance(tol));
+  BOOST_TEST(Y[0][1][1] == -1.0 / 2.0 * 2.0 * X[0][1][0] * X[0][1][0] -
+                               2.0 * test_in[0] * X[0][1][1],
+             tt::tolerance(tol));
+
+  // A == B, A < B
+  BOOST_TEST(Y[0][2][0] == -3 * std::pow(test_in[1], 2) * X[1][2][0],
+             tt::tolerance(tol));
+  BOOST_TEST(Y[0][2][1] ==
+                 -1.0 / 2.0 * 6.0 * test_in[1] * X[1][2][0] * X[1][2][0] -
+                     3.0 * std::pow(test_in[1], 2.0) * X[1][2][1],
+             tt::tolerance(tol));
+
+  myfree3(X);
+  myfree3(Y);
+}
 BOOST_AUTO_TEST_SUITE_END()
\ No newline at end of file