Haskell tips/why doesnt this scale linearly?

Question

My friend wrote a program which compares random arrangements of die faces to find the one with the most evenly distributed faces - especially when the faces are not a mere sequence.

I translated his program into haskell because I've been looking for a reason to talk someone's ear off about how cool haskell is. However, I am not very proficient with haskell (it took me forever to write this and it has undergone a couple giant refactorings) and so I have two problems.

1. he has been big on optimizing his versions, and this is not very fast, and it does not scale linearly. Did I mess up some tail recursion or is it some kind of larger problem?
2. the code that came out of this isn't actually as elegant as I had predicted. I know this isn't a discussion board, but if you have any ideas on how to simplify it I am all ears

This is the most relevant code:

-- _CENTERS :: [{ x :: Float, y :: Float, z :: Float}]
-- _VALUES :: [Num]

-- Basically just (repeat $ map rand [0.._SIDES]), but never using a seed twice
randstates from = (take _SIDES (infrand from)) : randstates newseed
    where   infrand seed = seed : infrand (shuffle seed)
            newseed      = (infrand from) !! (_SIDES + 1)

-- yates shuffle
yates _ (last:[]) = [last]
yates (rand:pass) (swap:order) = choice:yates pass rorder
        where   choice = order !! index
                index  = (randfrom rand) `mod` (length order)
                rorder = take (index) order ++ swap : drop (index + 1) order

arrangements seed = map arrange $ randstates seed
        where   arrange rands = yates rands [0.._SIDES - 2]

-- fns comparing arrangements --
arcLength i j = 1 / (1 + _WEIGHT * acos(dot3D / _VEC_LEN_SQUARED))
        where   dot3D    = apply x + apply y + apply z
                apply fn = (fn i) * (fn j)

matrix arr = map crosscmp arr
        where   crosscmp s1  = [ value s1 * (distance s1 s2) | s2  <- arr ]
                distance a b = arcLength (_CENTERS !! a) (_CENTERS !! b)
                value s      = fromInteger $ _VALUES !! s

variance arr = sum $ map perside (matrix arr)
        where   perside s = (sum s - mean) ^ 2
                mean      = (sum (concat $ matrix arr)) / (sides + 1)
                sides     = fromInteger $ toInteger _SIDES

maxDistr = maximumBy (\a b -> variance a `compare` variance b)

Main is basically just

print $ maxDistr $ take _TRIALS $ arrangements seed

Answer 1

As the comments note, it can't scale linearly as indexing into a list is O(index). You will need to move to an array structure to begin to see improvements.