>     (reduce #(+ %1 %2) 0 (map sum (range 1 (inc iterations))))

can be replaced by (reduce + (map sum (range 1 (inc iterations))))

There is at least some functions in clojure's api for doing unchecked
calculations. That should speed up things. I'm not yet familiar
enough
with clojure or building trees if there is some large algorithmic
difference
 between the java and the clojure version.

http://clojure.org/api
(unchecked-add x y)
(unchecked-dec x)
(unchecked-divide x y)
(unchecked-inc x)
(unchecked-multiply x y)
(unchecked-negate x)
(unchecked-subtract x y)


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