`yampa`: improve accuracy of `integral` about yampa HOT 14 OPEN

integral :: (Monad m, VectorSpace a s) => SF m a a
integral = integralFrom zeroVector

integralFrom :: (Monad m, VectorSpace a s) => a -> SF m a a
integralFrom a0 =
  zeroVector --> proc a -> do
    dt <- constM ask -< ()
    aPrev <- iPre zeroVector -< a
    accumulateWith (^+^) a0 -< (realToFrac dt / 2) *^ (a ^+^ aPrev)

integral :: forall a s . (Fractional s, VectorSpace a s) => SF a a
integral = SF {sfTF = tf0}
  where
    tf0 a0 = (integralAux igrl0 a0, igrl0)

    igrl0  = zeroVector

    integralAux :: a -> a -> SF' a a
    integralAux igrl a_prev = SF' tf -- True
      where
        tf :: DTime -> a -> (SF' a a, a)
        tf dt a = (integralAux igrl' a, igrl')
          where
            igrl' = igrl ^+^ (realToFrac dt / 2) *^ (a ^+^ a_prev)

fallingBall :: Monad m => Pos -> Vel -> SF m () (Pos, Vel)
fallingBall p0 v0 = proc () -> do
  let g = -9.81
  v <- arr (\x -> v0 + x) <<< integral -< g
  p <- arr (\y -> p0 + y) <<< integral -< v
  returnA -< (p,v)

bouncingBall :: Monad m => Double -> Double -> SF m () (Double, Double)
bouncingBall p0 v0 =
  switch (fallingBall p0 v0 >>> (arr id &&& hitFloor))
         (\(p,v) -> bouncingBall p (-v))

hitFloor :: Monad m => SF m (Double,Double) (Event (Double,Double))
hitFloor = arr $ \(p,v) ->
  if p < 0 && v < 0 then Event (p,v) else noEvent

fallingBall :: Monad m => Pos -> Vel -> SF m () (Pos, Vel)
fallingBall p0 v0 = proc () -> do
  let g = -9.81
  v <- arr (\x -> v0 + x) <<< integral -< g
  p <- arr (\y -> p0 + y) <<< integralLinear v0 -< v
  returnA -< (p,v)

integralLinear :: Monad m => Double -> SF m Double Double
integralLinear initial = average >>> integral
  where
    average = (arr id &&& iPre initial) >>^ (\(x, y) -> (x ^+^ y) ^/ 2)

fallingBall :: Double -> Double -> SF () (Double, Double)
fallingBall p0 v0 = proc () -> do
  let g = -9.81
  v <- arr (\x -> v0 + x) <<< integral -< g
  p <- arr (\y -> p0 + y) <<< integral -< v
  returnA -< (p,v)

bouncingBall :: Double -> Double -> SF () (Double, Double)
bouncingBall p0 v0 =
  switch (fallingBall p0 v0 >>> (arr id &&& hitFloor))
         (\(p,v) -> bouncingBall p (-v))

hitFloor :: SF (Double, Double) (Event (Double, Double))
hitFloor = arr $ \(p,v) ->
  if p < 0 && v < 0 then Event (p,v) else noEvent