M000000043

$$\pi=1036\arctan\left(\frac{2}{4989}\right)+5760\arctan\left(\frac{1}{2673}\right)+7224\arctan\left(\frac{1}{12943}\right)+1592\arctan\left(\frac{2}{296489}\right)+4324\arctan\left(\frac{2}{2885139}\right)-732\arctan\left(\frac{1}{1610057}\right)-2528\arctan\left(\frac{1}{103224943}\right)+1592\arctan\left(\frac{1}{18677233307}\right)$$
Compact formula1036[4989/2] + 5760[2673] + 7224[12943] + 1592[296489/2] + 4324[2885139/2] - 732[1610057] - 2528[103224943] + 1592[18677233307]
Lehmer's measure1.56837
References
Wetherfield, Michael Roby and Chien-Lih, Hwang. Computing pi: Lists of Machin-type (inverse cotangent) identities for pi/4, [Online; accessed 04-February-2024], 2013. [web.archive.org/web/20240204042153/http] [Found by Amrik Singh Nimbran on 11 September 2009.]