M000000131

$$\pi=304\arctan\left(\frac{1}{114}\right)+28\arctan\left(\frac{1}{239}\right)+96\arctan\left(\frac{1}{268}\right)-48\arctan\left(\frac{1}{247057}\right)-128\arctan\left(\frac{1}{740943}\right)$$
Compact formula304[114] + 28[239] + 96[268] - 48[247057] - 128[740943]
Lehmer's measure1.67425
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 Koepp in 1994.]