import Misc (partition)
import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
import qualified Algebra.ToInteger as ToInteger
import qualified Algebra.ToRational as ToRational
-- >>> simpson_1 f (-1) 1
-- 0.0
--
+-- >>> import Algebra.Absolute (abs)
-- >>> let f x = x^2
-- >>> let area = simpson_1 f (-1) 1
-- >>> abs (area - (2/3)) < 1/10^12
--
-- Examples:
--
+-- >>> import Algebra.Absolute (abs)
-- >>> let f x = x^4
-- >>> let area = simpson 10 f (-1) 1
-- >>> abs (area - (2/5)) < 0.0001
-- Note that the convergence here is much faster than the Trapezoid
-- rule!
--
+-- >>> import Algebra.Absolute (abs)
-- >>> let area = simpson 10 sin 0 pi
-- >>> abs (area - 2) < 0.00001
-- True