diff --git a/src/tests/util/interval/interval.cpp b/src/tests/util/interval/interval.cpp
index 7ef6a0e40..9dbeb1861 100644
--- a/src/tests/util/interval/interval.cpp
+++ b/src/tests/util/interval/interval.cpp
@@ -91,9 +91,78 @@ static void tst2() {
     lean_assert_eq(power(qi(), 2), qi(false, 0)); // (-oo, oo)^2 == [0, oo)
 }
 
+static void check_deps(bound_deps const & deps, bool l1 = false, bool u1 = false, bool l2 = false, bool u2 = false) {
+    lean_assert(l1 == dep_in_lower1(deps));
+    lean_assert(u1 == dep_in_upper1(deps));
+    lean_assert(l2 == dep_in_lower2(deps));
+    lean_assert(u2 == dep_in_upper2(deps));
+}
+
+static void check_lower_deps(interval_deps const & deps, bool l1 = false, bool u1 = false, bool l2 = false, bool u2 = false) {
+    check_deps(deps.m_lower_deps, l1, u1, l2, u2);
+}
+
+static void check_upper_deps(interval_deps const & deps, bool l1 = false, bool u1 = false, bool l2 = false, bool u2 = false) {
+    check_deps(deps.m_upper_deps, l1, u1, l2, u2);
+}
+
+static void tst3() {
+    qi i1(3, 10, false, true);
+    qi i2(-8, 2, true, false);
+    swap(i1, i2);
+    lean_assert_eq(i1, qi(-8, 2, true, false));
+    lean_assert_eq(i2, qi(3, 10, false, true));
+    lean_assert(!qi(2, 3, true, true).contains(qi()));
+    lean_assert(!qi(2, 10, true, true).contains(qi(0, 10, true, true)));
+    lean_assert(!qi(2, 10, true, true).contains(qi(2, 10, false, true)));
+    lean_assert(!qi(2, 10, true, true).contains(qi(true, 5)));
+    lean_assert(!qi(2, 10, true, true).contains(qi(5, 11, true, true)));
+    lean_assert(!qi(2, 10, true, true).contains(qi(5, 10, true, false)));
+    lean_assert(!i1.is_empty());
+    i1.set_empty();
+    lean_assert(i1.is_empty());
+    lean_assert(!i1.is_singleton());
+    lean_assert(!i2.is_singleton());
+    i1 = qi(4);
+    lean_assert(i1.is_singleton());
+    lean_assert(!qi(true, 1).before(qi(1, 2)));
+    std::cout << qi(3, true) << "\n";
+    lean_assert(!qi(1, 2).before(qi(3, true)));
+    lean_assert(qi(1, 2).before(qi(3, 4)));
+    interval_deps deps;
+    qi().neg_jst(deps);
+    lean_assert_eq(neg(qi()), qi());
+    check_lower_deps(deps);
+    check_upper_deps(deps);
+    std::cout << qi(1, true) << "\n";
+    qi(1, true).neg_jst(deps);
+    lean_assert_eq(neg(qi(1, true)), qi(true, -1));
+    check_lower_deps(deps, false, true);
+    check_upper_deps(deps);
+    qi(true, 1).neg_jst(deps);
+    lean_assert_eq(neg(qi(true, 1)), qi(-1, true));
+    check_lower_deps(deps);
+    check_upper_deps(deps, true, false);
+    qi(1, 3).neg_jst(deps);
+    check_lower_deps(deps, false, true);
+    check_upper_deps(deps, true, false);
+    qi(1, 3).add_jst(qi(2, 4), deps);
+    check_lower_deps(deps, true, false, true, false);
+    check_upper_deps(deps, false, true, false, true);
+    qi(1, 3).sub_jst(qi(2, 4), deps);
+    check_lower_deps(deps, true, false, false, true);
+    check_upper_deps(deps, false, true, true, false);
+    qi i3(0);
+    i3 *= mpq(3);
+    lean_assert_eq(i3, qi(0));
+    i3 /= mpq(4);
+    lean_assert_eq(i3, qi(0));
+}
+
 int main() {
     enable_trace("numerics");
     tst1();
     tst2();
+    tst3();
     return has_violations() ? 1 : 0;
 }
diff --git a/src/util/interval/interval.cpp b/src/util/interval/interval.cpp
index 1cfed59f6..a2a267108 100644
--- a/src/util/interval/interval.cpp
+++ b/src/util/interval/interval.cpp
@@ -130,7 +130,9 @@ bool interval<T>::contains(interval<T> const & b) const {
 
 template<typename T>
 bool interval<T>::is_empty() const {
-    return m_lower == m_upper && m_lower_open && m_upper_open && !m_lower_inf && !m_upper_inf;
+    return
+        (m_lower == m_upper && (m_lower_open || m_upper_open) && !m_lower_inf && !m_upper_inf) ||
+        (m_lower > m_upper && !m_lower_inf && !m_upper_inf);
 }
 
 template<typename T>