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Add me: Koka 

import std/num/float64

pub fun main()
  println("The " ++ (4.0 * pi(0, 0.0)).show)

fun pi(n: int, sum : float64): pure float64
  if 100_000_000 < n
  then sum
  else
    val n4 = n.float64 * 4.0;
    pi(n + 1, sum + 2.0 / ((n4 + 1.0) * (n4 + 3.0)))

nix$ time .koka/v3.0.4/cc-drelease/pi
The 3.1415926445762157
.koka/v3.0.4/cc-drelease/pi  0.08s user 0.00s system 96% cpu 0.089 total

Pharo 

PiFinder class>>#runTo: pairs

	| denominator currSum tmp |
	denominator := -1.
	currSum := 0.0.
	pairs timesRepeat: [
		denominator := denominator + 4.
		tmp := denominator asFloat.
		currSum := currSum + (2.0 / (tmp * (tmp - 2.0))) ].
	^ 4.0 * currSum

Add me: Factor

  • 2024-02-09
    golfed
USING: kernel math ;
IN: leibniz

: lpi ( num-of-pairs: integer -- pi )
  0.0 0 rot
  [ [ 4.0 * [ 3.0 + ] [ 1.0 + ] bi * 2.0 swap / + ] keep 1 + ] times
  drop 4 *
;
  • 2023-12-12
USING: kernel math ;
IN: Leibniz

: calcpi ( -- pi index )
    0.0 0
    [
        dup [ 4.0 * [ 3.0 + ] [ 1.0 + ] bi * 2.0 swap / + ] dip
　　　　　 1 +
　　　　　dup 100000000 <
    ] loop
    [ 4 * ] dip
    ! drop
    ;

100M pairs => 0.137 sec. on 2.3GHz dual core Core i5 😲

Add me: Lean4 

def leibniz (n : Nat) (sum : Float) : Float :=
  match n with
  | 0 => sum + 8.0 / 3.0
  | succ n' => let k := (n * 4).toFloat; leibniz n' (sum + 8.0 / ((k + 1.0) * (k + 3.0)))

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