Why is this F# code so slow?

Question

A Levenshtein implementation in C# and F#. The C# version is 10 times faster for two strings of about 1500 chars. C#: 69 ms, F# 867 ms. Why? As far as I can tell, they do the exact same thing? Doesn't matter if it is a Release or a Debug build.

EDIT: If anyone comes here looking specifically for the Edit Distance implementation, it is broken. Working code is here.

C#:

private static int min3(int a, int b, int c)
{
   return Math.Min(Math.Min(a, b), c);
}

public static int EditDistance(string m, string n)
{
   var d1 = new int[n.Length];
   for (int x = 0; x < d1.Length; x++) d1[x] = x;
   var d0 = new int[n.Length];
   for(int i = 1; i < m.Length; i++)
   {
      d0[0] = i;
      var ui = m[i];
      for (int j = 1; j < n.Length; j++ )
      {
         d0[j] = 1 + min3(d1[j], d0[j - 1], d1[j - 1] + (ui == n[j] ? -1 : 0));
      }
      Array.Copy(d0, d1, d1.Length);
   }
   return d0[n.Length - 1];
}

F#:

let min3(a, b, c) = min a (min b c)

let levenshtein (m:string) (n:string) =
   let d1 = Array.init n.Length id
   let d0 = Array.create n.Length 0
   for i=1 to m.Length-1 do
      d0.[0] <- i
      let ui = m.[i]
      for j=1 to n.Length-1 do
         d0.[j] <- 1 + min3(d1.[j], d0.[j-1], d1.[j-1] + if ui = n.[j] then -1 else 0)
      Array.blit d0 0 d1 0 n.Length
   d0.[n.Length-1]

Answer 1

The problem is that the min3 function is compiled as a generic function that uses generic comparison (I thought this uses just IComparable, but it is actually more complicated - it would use structural comparison for F# types and it's fairly complex logic).

> let min3(a, b, c) = min a (min b c);;
val min3 : 'a * 'a * 'a -> 'a when 'a : comparison

In the C# version, the function is not generic (it just takes int). You can improve the F# version by adding type annotations (to get the same thing as in C#):

let min3(a:int, b, c) = min a (min b c)

...or by making min3 as inline (in which case, it will be specialized to int when used):

let inline min3(a, b, c) = min a (min b c);;

For a random string str of length 300, I get the following numbers:

> levenshtein str ("foo" + str);;
Real: 00:00:03.938, CPU: 00:00:03.900, GC gen0: 275, gen1: 1, gen2: 0
val it : int = 3

> levenshtein_inlined str ("foo" + str);;
Real: 00:00:00.068, CPU: 00:00:00.078, GC gen0: 0, gen1: 0, gen2: 0
val it : int = 3