M000000352

$$\pi=5113917491406\arctan\left(\frac{1}{13502703082318}\right)-19592032281324\arctan\left(\frac{2}{28456536638489}\right)+7244495251948\arctan\left(\frac{1}{14483848717682}\right)+4337979822628\arctan\left(\frac{1}{15962244871097}\right)+56976087638296\arctan\left(\frac{2}{33377023452861}\right)+8737995238080\arctan\left(\frac{1}{20293776947868}\right)-12433590334510\arctan\left(\frac{1}{24405694099301}\right)-19470280104934\arctan\left(\frac{1}{33308851938318}\right)-24705254731190\arctan\left(\frac{1}{41887379804066}\right)+26821941103046\arctan\left(\frac{1}{42859110883727}\right)+3059210036814\arctan\left(\frac{1}{69971515635443}\right)-10161797458260\arctan\left(\frac{1}{83979525486773}\right)+90956470688156\arctan\left(\frac{1}{94465125845354}\right)+28486889778688\arctan\left(\frac{1}{127528611030443}\right)+84456956968212\arctan\left(\frac{1}{158682175700807}\right)-94057084887904\arctan\left(\frac{1}{187458398552950}\right)-94811336149606\arctan\left(\frac{1}{211773236092865}\right)-37843259686652\arctan\left(\frac{1}{240926005152903}\right)+93756062114216\arctan\left(\frac{1}{258213230677943}\right)-16985372322560\arctan\left(\frac{1}{317335434728073}\right)-76247830554906\arctan\left(\frac{1}{370392816588001}\right)-32199409338716\arctan\left(\frac{1}{758341235653128}\right)-21176828228548\arctan\left(\frac{1}{830202489183166}\right)-14596109667014\arctan\left(\frac{1}{971747796208283}\right)+16095620848104\arctan\left(\frac{1}{1143900177872158}\right)-19671506604544\arctan\left(\frac{1}{1427056404016693}\right)-551333736680\arctan\left(\frac{1}{2270451385422943}\right)+75996961656634\arctan\left(\frac{1}{4204987898062723}\right)+52408967323624\arctan\left(\frac{1}{6805164953551432}\right)+14596109667014\arctan\left(\frac{1}{1070716428239341129016693}\right)$$

Compact formula	5113917491406[13502703082318] - 19592032281324[28456536638489/2] + 7244495251948[14483848717682] + 4337979822628[15962244871097] + 56976087638296[33377023452861/2] + 8737995238080[20293776947868] - 12433590334510[24405694099301] - 19470280104934[33308851938318] - 24705254731190[41887379804066] + 26821941103046[42859110883727] + 3059210036814[69971515635443] - 10161797458260[83979525486773] + 90956470688156[94465125845354] + 28486889778688[127528611030443] + 84456956968212[158682175700807] - 94057084887904[187458398552950] - 94811336149606[211773236092865] - 37843259686652[240926005152903] + 93756062114216[258213230677943] - 16985372322560[317335434728073] - 76247830554906[370392816588001] - 32199409338716[758341235653128] - 21176828228548[830202489183166] - 14596109667014[971747796208283] + 16095620848104[1143900177872158] - 19671506604544[1427056404016693] - 551333736680[2270451385422943] + 75996961656634[4204987898062723] + 52408967323624[6805164953551432] + 14596109667014[1070716428239341129016693]
Lehmer's measure	2.09064
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 11 July 2009.] Download references as BibTeΧ