M000000364

$$\pi=6248909387356\arctan\left(\frac{1}{15962244871097}\right)+17815573438212\arctan\left(\frac{1}{20293776947868}\right)-4026920895044\arctan\left(\frac{2}{53518224361625}\right)+24899094133480\arctan\left(\frac{2}{56365016607239}\right)+20805595833368\arctan\left(\frac{1}{33308851938318}\right)+1960298362360\arctan\left(\frac{1}{41887379804066}\right)+32336761853680\arctan\left(\frac{1}{58705151760538}\right)-2325726539388\arctan\left(\frac{1}{69971515635443}\right)-21009597432552\arctan\left(\frac{1}{74285407663082}\right)+11118819059088\arctan\left(\frac{1}{83979525486773}\right)+3717679819640\arctan\left(\frac{1}{127528611030443}\right)+8277851010484\arctan\left(\frac{1}{158682175700807}\right)-10121729403052\arctan\left(\frac{2}{351408485766961}\right)-4485105608468\arctan\left(\frac{1}{187458398552950}\right)+8665771119424\arctan\left(\frac{1}{187530264407868}\right)+8967738834952\arctan\left(\frac{1}{211773236092865}\right)-11496385850632\arctan\left(\frac{1}{240926005152903}\right)+22910521843708\arctan\left(\frac{1}{258213230677943}\right)+4295244194788\arctan\left(\frac{1}{317335434728073}\right)-15186376614540\arctan\left(\frac{1}{370392816588001}\right)+4788163715832\arctan\left(\frac{1}{399185179810283}\right)-10510743364944\arctan\left(\frac{1}{594966589999007}\right)+14395819109068\arctan\left(\frac{1}{758341235653128}\right)-5073389388924\arctan\left(\frac{1}{830202489183166}\right)+1966677838864\arctan\left(\frac{1}{1086889881361383}\right)+1279862985276\arctan\left(\frac{1}{1143900177872158}\right)-21127464888172\arctan\left(\frac{1}{1427056404016693}\right)+1026330140292\arctan\left(\frac{1}{2270451385422943}\right)+18813115119860\arctan\left(\frac{1}{4204987898062723}\right)-10289699963784\arctan\left(\frac{1}{6805164953551432}\right)$$

Compact formula	6248909387356[15962244871097] + 17815573438212[20293776947868] - 4026920895044[53518224361625/2] + 24899094133480[56365016607239/2] + 20805595833368[33308851938318] + 1960298362360[41887379804066] + 32336761853680[58705151760538] - 2325726539388[69971515635443] - 21009597432552[74285407663082] + 11118819059088[83979525486773] + 3717679819640[127528611030443] + 8277851010484[158682175700807] - 10121729403052[351408485766961/2] - 4485105608468[187458398552950] + 8665771119424[187530264407868] + 8967738834952[211773236092865] - 11496385850632[240926005152903] + 22910521843708[258213230677943] + 4295244194788[317335434728073] - 15186376614540[370392816588001] + 4788163715832[399185179810283] - 10510743364944[594966589999007] + 14395819109068[758341235653128] - 5073389388924[830202489183166] + 1966677838864[1086889881361383] + 1279862985276[1143900177872158] - 21127464888172[1427056404016693] + 1026330140292[2270451385422943] + 18813115119860[4204987898062723] - 10289699963784[6805164953551432]
Lehmer's measure	2.09539
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 19 August 2011.] Download references as BibTeΧ