import Data.Ratio

f1, f2 :: (Num a) => a -> a
f1 x = x^3 + x - 5
f2 x = x^4 + 2*x - 5

euler :: (Rational -> Rational) -> Rational -> Rational -> [Rational]
euler f a b = xs
  where xs = a : b : map step (zip (tail xs) xs)
        step (x,x0) = x - (f x)*(x - x0) / (f x - f x0)

main = do
  putStrLn "1. f1(x) = x^3 + x - 5     [1,2]"
  mapM_ printResult . take 5 $ euler f1 1 2
  putStrLn "\n2. f2(x) = x^4 + 2*x - 5     [-2,-1]"
  mapM_ printResult . take 5 $ euler f2 (-2) (-1)
  putStrLn "\n3. f2(x) = x^4 + 2*x - 5     [1,2]"
  mapM_ printResult . take 5 $ euler f2 1 2
  
  
printResult :: Rational -> IO ()
printResult x = do
  putStr . show $ x
  putStr "  --->  "
  putStrLn . show $ (fromRational x :: Double)