module Main where

import Graphics.EasyPlot

-- Шаг сетки
delta = 0.001

-- Функция
u = sin

-- Точка
t = 0.5

-- Абсолютная погрешность
err = 10 ** (-3)

main :: IO ()
main = do
    let res = map (\(x,y) -> (fromIntegral x,y)) $ calc u t
    plot X11 $ Data2D [Style Lines] [] res 
    print res


calc u t = calc' 0 [] u t where
        calc' n stat u t | err' < err = (n, err') : stat
                         | otherwise = (n, err') : calc' (n + 1) stat u t
            where err' = abs (u t - maclaurin u t n) 

factorial n | n < 2 = 1
            | otherwise = n * factorial (n - 1)

diff u 0 h x = u x
diff u n h x = (u' (x + h) - u' (x - h)) / (2 * h) where
    u' = diff u (n - 1) h

maclaurin u x 0 = u 0
maclaurin u x n = (x ** (fromIntegral n)) * (diff u n delta 0) / (fromIntegral $ factorial n) + maclaurin u x (n - 1)