diff --git a/ChangeLog b/ChangeLog
index 5696431072..8bcc8b3ff2 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -3,6 +3,8 @@ Tue Mar  3 14:47:30 2015  Kazuki Tanaka  <gogotanaka@ruby-lang.org>
 	* math.c (num2dbl_with_to_f): direct casting from Rational to double.
 	  [Feature #10909]
 
+	* test/ruby/test_math.rb: add tests for the above change.
+
 Tue Mar  3 07:52:20 2015  Rei Odaira  <Rei.Odaira@gmail.com>
 
 	* test/ruby/test_symbol.rb: avoid a false positive in AIX.
diff --git a/test/ruby/test_math.rb b/test/ruby/test_math.rb
index 5073166363..b6f41ed357 100644
--- a/test/ruby/test_math.rb
+++ b/test/ruby/test_math.rb
@@ -42,6 +42,12 @@ class TestMath < Test::Unit::TestCase
     check(0.0,  Math.cos(2 * Math::PI / 4))
     check(-1.0, Math.cos(4 * Math::PI / 4))
     check(0.0,  Math.cos(6 * Math::PI / 4))
+    check(0.5403023058681398,  Math.cos(1))
+    check(-0.7112665029764864, Math.cos(1 << 62))
+    check(0.9289154176164999,  Math.cos((2 ** 62)/(3 ** 40).to_r))
+    check(0.9820680774815206,  Math.cos((2 ** 61)/(3 ** 40).to_r))
+    check(0.4194382061248139,  Math.cos((2 ** 62)/(3 ** 39).to_r))
+    check(0.8424482791616391,  Math.cos((2 ** 61)/(3 ** 39).to_r))
   end
 
   def test_sin
@@ -319,4 +325,19 @@ class TestMath < Test::Unit::TestCase
 
     Bignum.class_eval { alias to_f _to_f }
   end
+
+  def test_override_rational_to_f
+    Rational.class_eval do
+      alias _to_f to_f
+      def to_f
+        (self + 1)._to_f
+      end
+    end
+
+    check(Math.cos((0r + 1)._to_f), Math.cos(0r))
+    check(Math.exp((0r + 1)._to_f), Math.exp(0r))
+    check(Math.log((0r + 1)._to_f), Math.log(0r))
+
+    Rational.class_eval { alias to_f _to_f }
+  end
 end