let epsilon = 0.0001

let input _ = ()

let time t = t

let hybrid fsin  t =  s     where der s = cos t init 0.0
let hybrid fcos  t =     c  where der c = -. (sin t) init 1.0
let hybrid fboth t = (s, c) where (s, c) = (fsin t, fcos t)

let fsind  = Solve.solve_sundials(fsin)
let fcosd  = Solve.solve_sundials(fcos)
let fbothd = Solve.solve_sundials(fboth)

let hybrid sincos() =
  let rec der sin = cos    init 0.0
      and der cos = -. sin init 1.0
  in (sin, cos)

let sincos_ode45    = Solve.solve_ode45(sincos)
let sincos_sundials = Solve.solve_sundials(sincos)
let sincos_both     = Solve.synchr(sincos_ode45)(sincos_sundials)

let hybrid ball () =
  let rec der y  = y'    init 50.0 reset z -> 0.0
      and der y' = -9.81 init 0.0 reset z -> -0.8 *. (last y')
      and z = up(-. y)
  in y

let ball_ode45    = Solve.solve_ode45(ball)
let ball_sundials = Solve.solve_sundials(ball)
let ball_both     = Solve.synchr(ball_ode45)(ball_sundials)

let node print1 (now, v) =
  print_float(now); print_string "\t";
  print_float v; print_string "\n"

let node print2 (now, (l, r)) =
  print_float now; print_string "\t";
  print_float l; print_string "\t";
  print_float r; print_string "\n"

let node print22 (now, ((ll, rl), (lr, rr))) =
  print_float now;  print_string "\t";
  print_float ll; print_string "\t";
  print_float lr; print_string "\t";
  print_float rl; print_string "\t";
  print_float rr; print_string "\n"

let node check_sincos (now, (sin, cos)) =
  print2 (now, (sin, cos));
  sin <= 1.0 +. epsilon && sin >= -1.0 -. epsilon &&
  cos <= 1.0 +. epsilon && cos >= -1.0 -. epsilon

let node check_sincos2 (now, ((sin1, cos1), (sin2, cos2))) =
  print22 (now, ((sin1, cos1), (sin2, cos2)));
  sin1 <= 1.0 +. epsilon && sin1 >= -1.0 -. epsilon &&
  cos1 <= 1.0 +. epsilon && cos1 >= -1.0 -. epsilon &&
  sin2 <= 1.0 +. epsilon && sin2 >= -1.0 -. epsilon &&
  cos2 <= 1.0 +. epsilon && cos2 >= -1.0 -. epsilon

let node main() =
  let input = Some (Solve.make (100.0, time)) fby None in
  let o = run fbothd input in
  Solve.iter_t 100 print2 o