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import Control.Monad
import Data.List
import Text.Printf
eval' = foldr f
    where
    f 0 acc = acc + 2
    f 1 acc = sqrt acc
 
sol' = foldl' f
    where
    f acc 0 = acc - 2
    f acc 1 = acc ^2 
 
sol, eval :: [Int] -> Double
sol = sol' pi
eval = eval' 0
 
dfs :: [Int] -> Double -> IO ()
dfs key tgt 
    | eval key == pi = printf "find solution %d\n" (length key)
    | otherwise = do
        when (foldl' (\acc x -> acc * 3 + x) 0 key `mod` 1000 == 0) $ 
            printf "current context: %s %.15f\n" (show key) tgt
        let n = length key
        let good (key, v) = eval key == pi || (1 < v && v < fromIntegral (2 * (53 - n)))
        let cands = filter good [(key ++ [0], tgt - 2), (key ++ [1], tgt^2)]
        forM_ cands $ \(nkey, ntgt) -> dfs nkey ntgt
 
 
main :: IO ()
main = 
    dfs [] pi

Success #stdin #stdout 0.04s 0KB

stdin

Standard input is empty

stdout

current context: [] 3.141592653589793
current context: [0] 1.141592653589793
find solution 53
current context: [0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] 10.009967193484070
current context: [0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0] 8.009967193484070
current context: [0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0] 6.009967193484069
current context: [0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] 2.136979828787066
current context: [0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] 12.971464939400775
current context: [0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] 10.971464939400775
current context: [0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0,0] 8.971464939400775
current context: [0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0] 3.096778591615806
current context: [0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0] 1.096778591615806
current context: [0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,1] 1.055802708798190
current context: [0,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0] 9.249623879059596
current context: [1,0,0,0,0,1,0,1,1,0,1,0,0,0,0,1,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0] 2.248988542770825
current context: [1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1] 12.589836050062631
current context: [1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0] 10.589836050062631
current context: [1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0] 8.589836050062631
current context: [1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0] 1.135235828711170
current context: [1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0] 1.470652565890449

https://ideone.com/5WwNiY

language:

Haskell (ghc 8.4.4)

created:

visibility:

public

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