[Haskell-cafe] Another optimization question

[Jeroen]

Hi, I know there's been quite some performance/optimization post lately,
so I hope there still room for one more. While solving a ProjectEuler
problem (27), I saw a performance issue I cannot explain. I narrowed it
down to the following code (never mind that 'primes' is just [1..],
the problem is the same or worse with real primes):

primes :: [Int]
primes = [1..]

isPrime :: Int -> Bool
isPrime x = isPrime' x primes
    where isPrime' x (p:ps) | x == p = True
                            | x > p = isPrime' x ps
                            | otherwise = False

main = print $ length (filter (== True) (map isPrime [1..5000]))

$ time ./experiment1
5000

real	0m4.037s
user	0m3.378s
sys	0m0.060s


All good, but if I change isPrime to the simpeler

isPrime x = elem x (takeWhile (<= x) primes)

it takes twice as long:

time ./experiment2
5000

real	0m7.837s
user	0m6.532s
sys	0m0.141s

With real primes, it even takes 10 times as long.
I tried looking at the output of ghc -ddump-simpl,
as suggested in a previous post, but it's a bit over
my head (newby here...).

Any suggestions?

Thanks a lot,

Jeroen