M000000120

$$\pi=332\arctan\left(\frac{1}{239}\right)+752\arctan\left(\frac{1}{580}\right)+800\arctan\left(\frac{1}{1710}\right)-576\arctan\left(\frac{1}{91093}\right)-576\arctan\left(\frac{1}{103862}\right)-48\arctan\left(\frac{2}{2513489}\right)$$
Compact formula332[239] + 752[580] + 800[1710] - 576[91093] - 576[103862] - 48[2513489/2]
Lehmer's measure1.65656
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 MRW on 22 June 2009.]