094 Almost equilateral triangles.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 17 August 2016
# Translated: 21 March 2023
# https://github.com/trizen

# https://projecteuler.net/problem=94

# Runtime: 0.256s

var sum   = 0
var limit = 1_000_000_000

for (var n = 1; true; ++n) {

    var x = ((((7 - 4*sqrtQ(3))**n) + (7 + 4*sqrtQ(3))**n + 1) / 3)
    var y = (((sqrtQ(3) + 2)*(7 - 4*sqrtQ(3))**(n+1) - (sqrtQ(3) - 2)*(7 + 4*sqrtQ(3))**(n+1) - 1) / 3)

    var p1 = (3*x + 1)
    var p2 = (3*y - 1)

    break if ((p1 > limit) && (p2 > limit))

    sum += p1 if (p1 <= limit)
    sum += p2 if (p2 <= limit)
}

say sum.real