M000000327

$$\pi=4961125323376\arctan\left(\frac{1}{5727066010185}\right)+8743010208004\arctan\left(\frac{1}{5945958754193}\right)-1156828021768\arctan\left(\frac{1}{7601001102973}\right)-4368997619040\arctan\left(\frac{1}{7758917519457}\right)+4337979822628\arctan\left(\frac{1}{9952436262333}\right)+12665280191480\arctan\left(\frac{1}{10546511281730}\right)-5029830080620\arctan\left(\frac{1}{13502703082318}\right)+1365940073088\arctan\left(\frac{2}{28456536638489}\right)-1643915024828\arctan\left(\frac{1}{14483848717682}\right)-2184917152876\arctan\left(\frac{2}{33377023452861}\right)+2075564447048\arctan\left(\frac{1}{24405694099301}\right)+12246030819828\arctan\left(\frac{1}{41887379804066}\right)-5282601396956\arctan\left(\frac{1}{42859110883727}\right)-3749380286148\arctan\left(\frac{1}{69971515635443}\right)+7346635374728\arctan\left(\frac{1}{83979525486773}\right)+1569406192980\arctan\left(\frac{1}{94465125845354}\right)-2216915357292\arctan\left(\frac{1}{127528611030443}\right)+4550735247252\arctan\left(\frac{1}{187458398552950}\right)+4719475917596\arctan\left(\frac{1}{211773236092865}\right)+14314150927264\arctan\left(\frac{1}{317335434728073}\right)+1878281522320\arctan\left(\frac{1}{370392816588001}\right)+11761803693080\arctan\left(\frac{1}{758341235653128}\right)+4596869380468\arctan\left(\frac{1}{830202489183166}\right)+8364038593096\arctan\left(\frac{1}{1143900177872158}\right)-7155216891344\arctan\left(\frac{1}{1427056404016693}\right)-998061372244\arctan\left(\frac{1}{2270451385422943}\right)-6498148039632\arctan\left(\frac{1}{4204987898062723}\right)-6838992353004\arctan\left(\frac{1}{6805164953551432}\right)$$

Compact formula	4961125323376[5727066010185] + 8743010208004[5945958754193] - 1156828021768[7601001102973] - 4368997619040[7758917519457] + 4337979822628[9952436262333] + 12665280191480[10546511281730] - 5029830080620[13502703082318] + 1365940073088[28456536638489/2] - 1643915024828[14483848717682] - 2184917152876[33377023452861/2] + 2075564447048[24405694099301] + 12246030819828[41887379804066] - 5282601396956[42859110883727] - 3749380286148[69971515635443] + 7346635374728[83979525486773] + 1569406192980[94465125845354] - 2216915357292[127528611030443] + 4550735247252[187458398552950] + 4719475917596[211773236092865] + 14314150927264[317335434728073] + 1878281522320[370392816588001] + 11761803693080[758341235653128] + 4596869380468[830202489183166] + 8364038593096[1143900177872158] - 7155216891344[1427056404016693] - 998061372244[2270451385422943] - 6498148039632[4204987898062723] - 6838992353004[6805164953551432]
Lehmer's measure	2.01373
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 24 February 2004.] Download references as BibTeΧ