leibniz_formula.cljs

cljs.user=> (defn leibniz [n-terms]
       #_=>   (->> (iterate inc 1)
       #_=>        (filter odd?)
       #_=>        (map / (cycle [1 -1]))
       #_=>        (take n-terms)
       #_=>        (apply +)
       #_=>        (* 4.0)))
#'cljs.user/leibniz
cljs.user=> (time (leibniz 10000))
"Elapsed time: 51.138105 msecs"
3.1414926535900345
cljs.user=> (time (leibniz 100000))
"Elapsed time: 530.490666 msecs"
3.1415826535897198
cljs.user=> (time (leibniz 1000000))
"Elapsed time: 5867.103103 msecs"
3.1415916535897743
cljs.user=> (defn leibniz' [n-terms]
       #_=>   (->> (transduce
       #_=>         (take n-terms)
       #_=>         +
       #_=>         (->> (iterate #(+ % 2) 1)
       #_=>              (map / (cycle [1 -1]))))
       #_=>        (* 4.0)))
#'cljs.user/leibniz'
cljs.user=> (time (leibniz' 10000))
"Elapsed time: 46.125388 msecs"
3.1414926535900345
cljs.user=> (time (leibniz' 100000))
"Elapsed time: 357.253515 msecs"
3.1415826535897198
cljs.user=> (time (leibniz' 1000000))
"Elapsed time: 3433.809805 msecs"
3.1415916535897743
cljs.user=> (defn leibniz'' [n-terms]
       #_=>   (->> (iterate #(+ % 2) 1)
       #_=>        (map / (cycle [1 -1]))
       #_=>        (take n-terms)
       #_=>        (apply +)
       #_=>        (* 4.0)))
#'cljs.user/leibniz''
cljs.user=> (time (leibniz'' 10000))
"Elapsed time: 70.789558 msecs"
3.1414926535900345
cljs.user=> (time (leibniz'' 100000))
"Elapsed time: 456.015960 msecs"
3.1415826535897198
cljs.user=> (time (leibniz'' 1000000))
"Elapsed time: 4224.213782 msecs"
3.1415916535897743

cf. https://ja.wikipedia.org/wiki/ライプニッツの公式