(defn square [x] (* x x))

(defn good-enough2? [previous current acc]
  (>=
    (* current acc)
    (math/abs (- current previous))))

(defn good-enough? [guess x acc]
  (< (math/abs (- (square guess) x)) acc))

(defn average [x y]
  (/ (+ x y) 2))

(defn improve [guess x]
  (average guess (/ x guess)))

(defn sqrt-iter [guess x acc]
  (if (good-enough? guess x acc)
          guess
          (sqrt-iter (improve guess x) x acc)))

(defn sqrt-iter2 [prev guess x acc]
  (if (good-enough2? prev guess acc)
          guess
          (sqrt-iter2 guess (improve guess x) x acc)))

(defn sqrt-iter-max [guess x i acc]
  (if (= i 0)
    -1
    (if (good-enough? guess x acc)
          guess
          (sqrt-iter-max (improve guess x) x (- i 1) acc))))

(defn sqrt [x acc]
  (sqrt-iter 1.0 x acc))

(defn sqrt2 [x acc]
  (sqrt-iter2 0.0 x x acc))

(defn sqrt-max [x acc]
  (sqrt-iter-max 1.0 x 500 acc))

(defn relative-error [i f]
  (def measurement (sqrt2 i 0.0001))
  (def measurement2 (sqrt2 i 0.00001))
  (def measurement3 (sqrt2 i 0.000001))
  (def actual (math/sqrt i))
  (def rel-error (/ (- measurement actual) measurement))
  (def rel-error2 (/ (- measurement2 actual) measurement2))
  (def rel-error3 (/ (- measurement3 actual) measurement3))
  (file/write f (string/format "%e,%e,%e,%e\n" i rel-error rel-error2 rel-error3)))

(defn find-breakpoint []
  (var found? false)
  (var base 1.0e12)
  (var minimum 1.0e-3)
  (var num 0.0)
  (while (not found?)
    (def test (+ num base))
    (if (>= (sqrt-max test 0.001) 0)
      (set num (+ num base))
      (do
        (set base (/ base 10.0))
        (if (< base minimum)
          (set found? true)))))
  num)

(print (find-breakpoint))

(def f (file/open "exercise_1_7_data.csv" :w))
(file/write f "i,0.001,0.0001,0.00001\n")
(var total (* 2 50))
(var num 1e25)
(while (> total 0)
  (relative-error num f)
  (set num (/ num (math/sqrt 10.0)))
  (set total (- total 1)))

(file/close f)