M000000338

$$\pi=-14596109667014\arctan\left(\frac{2}{23780027088431}\right)+5113917491406\arctan\left(\frac{1}{13502703082318}\right)-4995922614310\arctan\left(\frac{2}{28456536638489}\right)+7244495251948\arctan\left(\frac{1}{14483848717682}\right)+4337979822628\arctan\left(\frac{1}{15962244871097}\right)+42379977971282\arctan\left(\frac{2}{33377023452861}\right)+23334104905094\arctan\left(\frac{1}{20293776947868}\right)+2162519332504\arctan\left(\frac{1}{24405694099301}\right)-19470280104934\arctan\left(\frac{1}{33308851938318}\right)-24705254731190\arctan\left(\frac{1}{41887379804066}\right)+26821941103046\arctan\left(\frac{1}{42859110883727}\right)+3059210036814\arctan\left(\frac{1}{69971515635443}\right)-10161797458260\arctan\left(\frac{1}{83979525486773}\right)+47168141687114\arctan\left(\frac{1}{94465125845354}\right)+13890780111674\arctan\left(\frac{1}{127528611030443}\right)+55264737634184\arctan\left(\frac{1}{158682175700807}\right)-50268755886862\arctan\left(\frac{1}{187458398552950}\right)-51023007148564\arctan\left(\frac{1}{211773236092865}\right)-23247150019638\arctan\left(\frac{1}{240926005152903}\right)+64563842780188\arctan\left(\frac{1}{258213230677943}\right)-16985372322560\arctan\left(\frac{1}{317335434728073}\right)-47055611220878\arctan\left(\frac{1}{370392816588001}\right)-17603299671702\arctan\left(\frac{1}{758341235653128}\right)-6580718561534\arctan\left(\frac{1}{830202489183166}\right)+16095620848104\arctan\left(\frac{1}{1143900177872158}\right)-5075396937530\arctan\left(\frac{1}{1427056404016693}\right)-551333736680\arctan\left(\frac{1}{2270451385422943}\right)+61400851989620\arctan\left(\frac{1}{4204987898062723}\right)+23216747989596\arctan\left(\frac{1}{6805164953551432}\right)$$

Compact formula	- 14596109667014[23780027088431/2] + 5113917491406[13502703082318] - 4995922614310[28456536638489/2] + 7244495251948[14483848717682] + 4337979822628[15962244871097] + 42379977971282[33377023452861/2] + 23334104905094[20293776947868] + 2162519332504[24405694099301] - 19470280104934[33308851938318] - 24705254731190[41887379804066] + 26821941103046[42859110883727] + 3059210036814[69971515635443] - 10161797458260[83979525486773] + 47168141687114[94465125845354] + 13890780111674[127528611030443] + 55264737634184[158682175700807] - 50268755886862[187458398552950] - 51023007148564[211773236092865] - 23247150019638[240926005152903] + 64563842780188[258213230677943] - 16985372322560[317335434728073] - 47055611220878[370392816588001] - 17603299671702[758341235653128] - 6580718561534[830202489183166] + 16095620848104[1143900177872158] - 5075396937530[1427056404016693] - 551333736680[2270451385422943] + 61400851989620[4204987898062723] + 23216747989596[6805164953551432]
Lehmer's measure	2.05879
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 18 February 2005.] Download references as BibTeΧ