Pi Calculation

This simple example implements the calculation of pi using the Gregory-Leibniz series

\[ \frac{pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-...=\sum_{k=0}^{\infty}\frac{(-1)^k}{2k+1} \]

The sum is computed for various number of terms from 10000000 to 200000000

benchmark(br, run(10000000, compute_pi))
benchmark(br, run(100000000, compute_pi))
benchmark(br, run(200000000, compute_pi))

The results are as follows:

Method Name	Mean	Standard Deviation
compute_pi(10000000)	86.675 ms	+/- 5.592 ms
compute_pi(100000000)	849.100 ms	+/- 25.177 ms
compute_pi(200000000)	1.708 s	+/- 0.047 s