Which Function is the best in terms of Stack Usage Efficiency and Time

Question

I wrote 3 functions that count the number of times an-element appears in a-list. I tried various inputs and profiled it but I still dont know which function is the best in terms of stack usage efficiency and time efficiency. Please Help me out.

;; Using an accumulator
    (defn count-instances1 [a-list an-element]
      (letfn [(count-aux [list-aux acc]
                         (cond
                           (empty? list-aux) acc
                           :else (if (= (first list-aux) an-element)  
                                   (count-aux (rest list-aux) (inc acc))
                                   (count-aux (rest list-aux) acc))))]
        (count-aux a-list 0)))

;; Normal counting 
    (defn count-instances2 [a-list an-element]
     (cond
       (empty? a-list) 0
       :else
          (if (= (first a-list) an-element )
              (+ 1 (count-instances2 (rest a-list) an-element))
              (count-instances2 (rest a-list) an-element))))

;; using loop. does this help at all?
   (defn count-instances3 [a-list an-element]
        (loop [mylist a-list acount 0]
            (if (empty? mylist)
                acount
                (if (= (first mylist) an-element)
                (recur (rest mylist)(inc acount))
                (recur (rest mylist) acount)))))

Answer 1

The loop/recur version is the right way. Clojure cannot optimize tail calls due to limitations of the JVM.