diff --git a/README.md b/README.md
index 9c91b4e..686ccf4 100644
--- a/README.md
+++ b/README.md
@@ -44,7 +44,7 @@ structure Expect:
     val error: exn -> (unit -> 'a) -> expectation
     datatype expectation = Fail of string * string | Pass
     val falsy: bool -> expectation
-    val nearTo: real -> real -> expectation
+    val nearTo: real -> real -> real -> expectation
     val truthy: bool -> expectation
   end
 structure Test:
@@ -76,7 +76,7 @@ val testsuite =
       (fn _ => bar () |> Expect.truthy),
     
     test "something that baz does"
-      (fn _ => baz (123) |> Expect.nearTo 123.10),
+      (fn _ => baz (123) |> Expect.nearTo 0.001 123.10),
     
     test "an exception from 'qux'"
       (fn _ => (fn _ => qux (0, 0))) |> Expect.error QuxError),
diff --git a/bin/generate b/bin/generate
index 3156055..c344f40 100755
--- a/bin/generate
+++ b/bin/generate
@@ -204,7 +204,7 @@ def expectation(signature, fn, args, expected, force=False):
     if signature['output'] == 'real':
         return tmpl % (
             invocation,
-            'nearTo %s' % output
+            'nearTo 0.001 %s' % output
         )
     return tmpl % (
         invocation,
diff --git a/exercises/practice/accumulate/testlib.sml b/exercises/practice/accumulate/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/accumulate/testlib.sml
+++ b/exercises/practice/accumulate/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/all-your-base/testlib.sml b/exercises/practice/all-your-base/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/all-your-base/testlib.sml
+++ b/exercises/practice/all-your-base/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/allergies/testlib.sml b/exercises/practice/allergies/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/allergies/testlib.sml
+++ b/exercises/practice/allergies/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/anagram/testlib.sml b/exercises/practice/anagram/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/anagram/testlib.sml
+++ b/exercises/practice/anagram/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/atbash-cipher/testlib.sml b/exercises/practice/atbash-cipher/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/atbash-cipher/testlib.sml
+++ b/exercises/practice/atbash-cipher/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/binary/testlib.sml b/exercises/practice/binary/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/binary/testlib.sml
+++ b/exercises/practice/binary/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/bob/testlib.sml b/exercises/practice/bob/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/bob/testlib.sml
+++ b/exercises/practice/bob/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/collatz-conjecture/testlib.sml b/exercises/practice/collatz-conjecture/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/collatz-conjecture/testlib.sml
+++ b/exercises/practice/collatz-conjecture/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/diamond/testlib.sml b/exercises/practice/diamond/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/diamond/testlib.sml
+++ b/exercises/practice/diamond/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/difference-of-squares/testlib.sml b/exercises/practice/difference-of-squares/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/difference-of-squares/testlib.sml
+++ b/exercises/practice/difference-of-squares/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/flatten-array/testlib.sml b/exercises/practice/flatten-array/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/flatten-array/testlib.sml
+++ b/exercises/practice/flatten-array/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/hamming/testlib.sml b/exercises/practice/hamming/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/hamming/testlib.sml
+++ b/exercises/practice/hamming/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/hello-world/testlib.sml b/exercises/practice/hello-world/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/hello-world/testlib.sml
+++ b/exercises/practice/hello-world/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/leap/testlib.sml b/exercises/practice/leap/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/leap/testlib.sml
+++ b/exercises/practice/leap/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/list-ops/testlib.sml b/exercises/practice/list-ops/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/list-ops/testlib.sml
+++ b/exercises/practice/list-ops/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/matching-brackets/testlib.sml b/exercises/practice/matching-brackets/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/matching-brackets/testlib.sml
+++ b/exercises/practice/matching-brackets/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/nth-prime/testlib.sml b/exercises/practice/nth-prime/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/nth-prime/testlib.sml
+++ b/exercises/practice/nth-prime/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/pangram/testlib.sml b/exercises/practice/pangram/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/pangram/testlib.sml
+++ b/exercises/practice/pangram/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/perfect-numbers/testlib.sml b/exercises/practice/perfect-numbers/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/perfect-numbers/testlib.sml
+++ b/exercises/practice/perfect-numbers/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/phone-number/testlib.sml b/exercises/practice/phone-number/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/phone-number/testlib.sml
+++ b/exercises/practice/phone-number/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/pig-latin/testlib.sml b/exercises/practice/pig-latin/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/pig-latin/testlib.sml
+++ b/exercises/practice/pig-latin/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/prime-factors/testlib.sml b/exercises/practice/prime-factors/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/prime-factors/testlib.sml
+++ b/exercises/practice/prime-factors/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/raindrops/testlib.sml b/exercises/practice/raindrops/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/raindrops/testlib.sml
+++ b/exercises/practice/raindrops/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/rna-transcription/testlib.sml b/exercises/practice/rna-transcription/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/rna-transcription/testlib.sml
+++ b/exercises/practice/rna-transcription/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/roman-numerals/testlib.sml b/exercises/practice/roman-numerals/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/roman-numerals/testlib.sml
+++ b/exercises/practice/roman-numerals/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/sum-of-multiples/testlib.sml b/exercises/practice/sum-of-multiples/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/sum-of-multiples/testlib.sml
+++ b/exercises/practice/sum-of-multiples/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/exercises/practice/two-fer/testlib.sml b/exercises/practice/two-fer/testlib.sml
index b9291bc..0c8370c 100644
--- a/exercises/practice/two-fer/testlib.sml
+++ b/exercises/practice/two-fer/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (
diff --git a/lib/testlib.sml b/lib/testlib.sml
index b9291bc..0c8370c 100644
--- a/lib/testlib.sml
+++ b/lib/testlib.sml
@@ -26,10 +26,11 @@ struct
       then Pass
       else failEq (PolyML.makestring b) (PolyML.makestring a)
 
-    fun nearTo b a =
-      if Real.== (a, b)
+    fun nearTo delta b a =
+      if Real.abs (a - b) <= delta * Real.abs a orelse
+         Real.abs (a - b) <= delta * Real.abs b
       then Pass
-      else failEq (Real.toString b) (Real.toString a)
+      else failEq (Real.toString b ^ " +/- " ^ Real.toString delta) (Real.toString a)
 
     fun anyError f =
       (