(def tolerance 0.00001)

(defn fixed-point [f damping first-guess]
  (defn close-enough? [v1 v2]
    (< (math/abs (- v1 v2))
       tolerance))
  (defn try-it [guess]
    (printf "current guess %f" guess)
    (let [next (damping guess (f guess))]
      (if (close-enough? guess next)
        next
        (try-it next))))
  (try-it first-guess))

(print "undamped")
(print (fixed-point 
         (fn [x] (/ (math/log 1000) (math/log x)))
         (fn [x1 x2] x2) 
         2.0
       )
)
(print "damped")
(print (fixed-point
         (fn [x] (/ (math/log 1000) (math/log x)))
         (fn [x1 x2] (* 0.5 (+ x1 x2)))
         2.0
        )
)