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. It goes from 415 checks/s to 97 checks/s when I go from 1000 to 20000 checks. 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 want this to be a solid showcase of Haskell, 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

Just a quick observation: as the length of values and centers increase, the list indexes (!!) are increasingly inefficient. Try values :: Vector Float, centers :: Vector Center with Data.Vector.(!) and see if performance improves.

I'm trying to see what other improvements can be made, I have a few in mind but its difficult to understand how your code works without the full program. Would you mind linking to a pastebin?