to start from the start, or from squares in bounded trial divisions sieve, does it change the complexity?

where-to-start.hs

-- http://stackoverflow.com/a/1510186/849891

-- does it change the complexity, where to start from ....?    -- make an empirical observation:

{-# OPTIONS_GHC -O2 #-}

g n = let { 
   svs = takeWhile ((< n).(^2).head) $ sv [2..]; 
   ps = map head svs; 
   qs = map (^2) ps; 
   a = map length $ map (takeWhile (< n)) svs;          -- whole length below `N`
   b = map length $ zipWith (takeWhile . (>)) qs svs    -- just to the square of head
  } in
      (sum a, sum b)

h :: Integral a=>(a,a)-> Float
h (a,b) = fromIntegral a/fromIntegral b

sv (x:xs) = (x:xs) : sv [y|y<-xs,rem y x /= 0]

{- Prelude> mapM_ print $ take 6 $ map (take 20) $ sv [2..]
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
[3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41]
[5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,55,59,61]
[7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77]
[11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89]
[13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
-}

main = 
  mapM_ (\x-> print (x,(h.g) x)) [ -- 10000,20000,40000,60000,80000,100000,120000,140000,
                                   -- 160000,200000,300000,400000, 700000  -- 1000000 
                                   2000000]
{-
(  10000,6.0307)       -- wasted effort is 1/6th,  getting to the upper limit  N=10,000
(  20000,5.334525)
(  40000,4.780339)
(  60000,4.9264565)         --     emp.ord.grw.,  optimal:
(  80000,4.769512)          -- 10k: X, 1mln: Y,  ~ log (Y*(1-1/4.4)/X*(1-1/6)) / log(100) in `N`
( 100000,4.857076)          --                   ~ log (Y*(1-1/4.4)/X*(1-1/6)) / log(100*2/3) in `n`
( 120000,5.1768265)         --  w/wasted effort:    log(Y/X) / log(100)
( 140000,4.838724)          --                      log(Y/X) / log(66.6)    (63.9 actually)
( 160000,4.8267465) 
( 200000,4.6948023)    -- additional complexity                         _____________
( 300000,4.7028465)    --  in N: log( 0.8333333/0.7727272 ) / log(100)   ~ 0.016396  |
( 400000,4.5043993)    --  in n: log( 0.8333333/0.7727272 ) / log(63.9)  ~ 0.018163  |
( 700000,4.4351783)                                             --      ~~~~~~~~~~~~~/
(1000000,4.393456)     -- wasted effort is 1/4.4th,  getting to the upper limit  N=1,000,000
   -- a giant space leak...
-}
-- mentioned at http://stackoverflow.com/questions/20921134/
--  is-there-in-the-world-any-strong-optimizing-compiler-for-a-simple-functional-lan
--  #comment31418410_20921134