M000003546
$$\pi=-32\arctan\left(\frac{1}{2}\right)+64\arctan\left(\frac{1}{5}\right)+32\arctan\left(\frac{1}{12}\right)+64\arctan\left(\frac{1}{21}\right)-32\arctan\left(\frac{1}{70}\right)+12\arctan\left(\frac{1}{239}\right)+16\arctan\left(\frac{2}{695}\right)+16\arctan\left(\frac{1}{724196}\right)$$