[Haskell-cafe] Mysterious factorial

Why fact2 is quicker than fact?! fact2 :: Integer -> Integer fact2 x = f x y where f n e | n < 2 = 1 | e == 0 = n * (n - 1) | e > 0 = (f n (e `div` 2)) * (f (n - (e * 2)) (e `div` 2)) y = 2 ^ (truncate (log (fromInteger x) / log 2)) fact :: Integer -> Integer fact 1 = 1 fact n = n * fact (n - 1) I tried to write tail-recursive fact, fact as "product [1..n]" - fact2 is quicker! fact2 1000000 == fact 1000000 - I tested.