M000000173

$$\pi=76\arctan\left(\frac{1}{24}\right)-16\arctan\left(\frac{1}{882}\right)-36\arctan\left(\frac{1}{6948}\right)+4\arctan\left(\frac{1}{43691}\right)-4\arctan\left(\frac{1}{308142}\right)$$
Compact formula76[24] - 16[882] - 36[6948] + 4[43691] - 4[308142]
Lehmer's measure1.72201
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 Matsumoto in 2000.]