M000000310

$$\pi=64\arctan\left(\frac{1}{20}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-64\arctan\left(\frac{1}{8040}\right)+32\arctan\left(\frac{1}{1620050}\right)$$
Compact formula64[20] - 4[239] - 16[515] - 64[8040] + 32[1620050]
Lehmer's measure1.97493
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 E.-B. Escott in 1903.]