@@ -0,0 +1,75 @@
+//
+// Copyright (c) 2019-2022 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using AngouriMath;
+using AngouriMath.Extensions;
+using Xunit;
+
+namespace AngouriMath.Tests.Common
+{
+    /// <summary>
+    /// Intersections and unions of intervals were left as written.
+    /// https://github.com/asc-community/AngouriMath/issues/415
+    /// </summary>
+    /// <remarks>
+    /// The behaviour was fixed by PR #677, but the example the issue actually reports -- a
+    /// screenshot, which is why it was easy to skip -- was never among the cases tested. An
+    /// intersection of my own choosing was tested instead, and the maintainer said so on the
+    /// issue. This pins the reporter's expression, character for character.
+    /// </remarks>
+    public sealed class IntervalSimplificationTest
+    {
+        /// <summary>
+        /// The expression from the screenshot on #415, in the syntax it was written in.
+        /// <code>
+        ///     (-1; 1) /\ (((-(sqrt(33) + 3)) / 6; (sqrt(33) - 3) / 6) \/ (1; +oo))
+        /// </code>
+        /// The left endpoint of the inner interval is about -1.457 and the right about
+        /// 0.457, so intersecting with (-1; 1) keeps (-1; (sqrt(33) - 3) / 6), and the
+        /// (1; +oo) branch contributes nothing.
+        /// </summary>
+        [Fact]
+        public void TheReportersOwnExample()
+        {
+            var simplified = @"(-1; 1) /\ (((-(sqrt(33) + 3)) / 6; (sqrt(33) - 3) / 6) \/ (1; +oo))"
+                .ToEntity().Simplify();
+            Assert.Equal(@"(-1; (sqrt(33) - 3) / 6)".ToEntity(), simplified);
+        }
+
+        /// <summary>
+        /// The endpoints are surds, and the comparison that decides the intersection has to
+        /// evaluate them rather than compare them as written -- which is what PR #677 fixed.
+        /// Checked by membership rather than by shape, so that a differently spelled but
+        /// equal answer still passes and a wrong one still fails.
+        /// </summary>
+        [Theory]
+        [InlineData("-0.9", true)]
+        [InlineData("0", true)]
+        [InlineData("0.45", true)]
+        [InlineData("0.46", false)]   // just past (sqrt(33) - 3) / 6 = 0.4574...
+        [InlineData("-1", false)]     // open at the left end
+        [InlineData("0.99", false)]
+        [InlineData("2", false)]      // the (1; +oo) branch is cut away by (-1; 1)
+        public void TheAnswerHoldsTheRightPoints(string point, bool expected)
+        {
+            var simplified = (Entity.Set)@"(-1; 1) /\ (((-(sqrt(33) + 3)) / 6; (sqrt(33) - 3) / 6) \/ (1; +oo))"
+                .ToEntity().Simplify();
+            Assert.Equal(expected, simplified.Contains(point.ToEntity()));
+        }
+
+        /// <summary>
+        /// Intersection distributing over a union, which is the other half of what PR #677
+        /// had to add for the example above to reduce at all.
+        /// </summary>
+        [Theory]
+        [InlineData(@"[3; 7] \/ [5; 10]", "[3; 10]")]
+        [InlineData(@"[1; 5] /\ [3; 8]", "[3; 5]")]
+        [InlineData(@"[0; 10] /\ ([1; 2] \/ [3; 4])", @"[1; 2] \/ [3; 4]")]
+        public void IntervalsCombine(string expr, string expected)
+            => Assert.Equal(expected.ToEntity().Simplify(), expr.ToEntity().Simplify());
+    }
+}