M000000221

$$\pi=152\arctan\left(\frac{1}{47}\right)+28\arctan\left(\frac{1}{239}\right)-56\arctan\left(\frac{1}{268}\right)-48\arctan\left(\frac{1}{247057}\right)+24\arctan\left(\frac{1}{740943}\right)$$
Compact formula152[47] + 28[239] - 56[268] - 48[247057] + 24[740943]
Lehmer's measure1.78613
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.]