Approx e^x with taylor

exp.fsx

let fact x =
  let rec fact_r x acc =
    match x with
    | 1.0 -> acc
    | y -> fact_r (x - 1.0) (acc * x)
  fact_r x 1.0

let expo x k =
  let rec expo_r x k acc =
    match k with
    | 0 -> acc
    | y -> expo_r x (k - 1) (acc * x)
  expo_r x k 1.0

let f x k =
  let rec f_r x k acc =
    match k with
    | 0 -> acc + 1.0
    | y -> f_r x (k - 1) (acc + ((expo x k) / fact k))
  f_r x k 0

let apprTaylor x =
  Seq.initInfinite (fun v -> f x v)

let apprExp x delta =
  let a = apprTaylor x
  let rec appr_r x delta i =
    if abs((Seq.item (i + 1) a) - (Seq.item i a)) < delta then
      Seq.item i a
    else
      appr_r x delta (i + 1)
  appr_r x delta 0