Estimation of π using Leibniz series

[alfrednewman]

Hello,

How can I optimize the speed of the following proc:
    
    
    import times, math
    
    proc leibniz(terms: int): float =
        var res = 0.0
        for n in 0..terms:
            res += pow(-1.0,float(n))/(2.0*float(n)+1.0)
        return 4*res
    
    let t0 = cpuTime()
    echo(leibniz(100_000_000))
    let t1 = cpuTime()
    echo "Elapsed time: ", $(t1 - t0)
    

I have the following result in my computer: 3.141592663589326 Elapsed time: 8.23

This result is almost 5x faster than my CPython counter party, but on the other 
hand it is around 6x slower than Julia, given the following code: 
    
    
    function leibniz(terms)
      res = 0.0
      for i in 0:terms
        res += (-1.0)^i/(2.0*i+1.0)
      end
      return res *= 4.0
    end
    
    println("Pi: ", @time leibniz(100_000_000))
    

1.374829 seconds (1.72 k allocations: 90.561 KiB) Pi: 3.141592663589326