M000000356

$$\pi=30548305295468\arctan\left(\frac{1}{20293776947868}\right)-2672172385516\arctan\left(\frac{1}{33118869842107}\right)-11492664470148\arctan\left(\frac{1}{33308851938318}\right)-4455974699724\arctan\left(\frac{1}{38057255532937}\right)+36768921384720\arctan\left(\frac{1}{41887379804066}\right)+41335690243096\arctan\left(\frac{1}{68626143507693}\right)-29019402070888\arctan\left(\frac{1}{69971515635443}\right)+16722976711308\arctan\left(\frac{1}{71736735559237}\right)+24240564878236\arctan\left(\frac{1}{83979525486773}\right)+7244495251948\arctan\left(\frac{1}{114011218145573}\right)-15397664733416\arctan\left(\frac{1}{127528611030443}\right)+46554001616560\arctan\left(\frac{1}{158682175700807}\right)+14565814805440\arctan\left(\frac{1}{159773026302313}\right)+26531865864828\arctan\left(\frac{1}{180481359172943}\right)+24175247761896\arctan\left(\frac{1}{187458398552950}\right)+19277154219728\arctan\left(\frac{1}{199921633110818}\right)+4240745050432\arctan\left(\frac{1}{211773236092865}\right)-32623869742516\arctan\left(\frac{1}{240926005152903}\right)+12716259063524\arctan\left(\frac{1}{258213230677943}\right)-6859823785496\arctan\left(\frac{1}{317335434728073}\right)-4675633249596\arctan\left(\frac{1}{370392816588001}\right)-22253355202008\arctan\left(\frac{1}{372274117624457}\right)+21794985279104\arctan\left(\frac{1}{758341235653128}\right)-3806784439536\arctan\left(\frac{1}{830202489183166}\right)+2687880816864\arctan\left(\frac{1}{977167012914932}\right)+30030077007188\arctan\left(\frac{1}{1143900177872158}\right)+16893375064456\arctan\left(\frac{1}{1427056404016693}\right)-39216498304648\arctan\left(\frac{1}{2270451385422943}\right)+14457780155496\arctan\left(\frac{1}{4204987898062723}\right)+8009223533088\arctan\left(\frac{1}{6805164953551432}\right)$$

Compact formula	30548305295468[20293776947868] - 2672172385516[33118869842107] - 11492664470148[33308851938318] - 4455974699724[38057255532937] + 36768921384720[41887379804066] + 41335690243096[68626143507693] - 29019402070888[69971515635443] + 16722976711308[71736735559237] + 24240564878236[83979525486773] + 7244495251948[114011218145573] - 15397664733416[127528611030443] + 46554001616560[158682175700807] + 14565814805440[159773026302313] + 26531865864828[180481359172943] + 24175247761896[187458398552950] + 19277154219728[199921633110818] + 4240745050432[211773236092865] - 32623869742516[240926005152903] + 12716259063524[258213230677943] - 6859823785496[317335434728073] - 4675633249596[370392816588001] - 22253355202008[372274117624457] + 21794985279104[758341235653128] - 3806784439536[830202489183166] + 2687880816864[977167012914932] + 30030077007188[1143900177872158] + 16893375064456[1427056404016693] - 39216498304648[2270451385422943] + 14457780155496[4204987898062723] + 8009223533088[6805164953551432]
Lehmer's measure	2.09216
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