M000000202

$$\pi=137352596\arctan\left(\frac{2}{322564791}\right)+289300084\arctan\left(\frac{1}{201229582}\right)+185011632\arctan\left(\frac{1}{284862638}\right)+29002772\arctan\left(\frac{1}{353566973}\right)+62315684\arctan\left(\frac{1}{546365045}\right)-60591224\arctan\left(\frac{1}{1514342682}\right)+29427040\arctan\left(\frac{2}{3340159163}\right)-30640352\arctan\left(\frac{2}{4204410541}\right)+71870436\arctan\left(\frac{2}{11352069609}\right)+199529104\arctan\left(\frac{1}{6421564557}\right)-37581644\arctan\left(\frac{1}{7427844818}\right)+78446220\arctan\left(\frac{1}{7959681215}\right)+12625764\arctan\left(\frac{2}{75525552427}\right)-237595084\arctan\left(\frac{2}{108928448489}\right)-117283892\arctan\left(\frac{1}{164432798314}\right)-42576636\arctan\left(\frac{2}{1087840667761}\right)-202907840\arctan\left(\frac{1}{169838669284032}\right)$$

Compact formula	`137352596[322564791/2] + 289300084[201229582] + 185011632[284862638] + 29002772[353566973] + 62315684[546365045] - 60591224[1514342682] + 29427040[3340159163/2] - 30640352[4204410541/2] + 71870436[11352069609/2] + 199529104[6421564557] - 37581644[7427844818] + 78446220[7959681215] + 12625764[75525552427/2] - 237595084[108928448489/2] - 117283892[164432798314] - 42576636[1087840667761/2] - 202907840[169838669284032]`
Lehmer's measure	1.75572
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 12 August 2006.] Download references as BibTeΧ