M000000321

$$\pi=1774431961956\arctan\left(\frac{1}{1737653394482}\right)+2048633606808\arctan\left(\frac{1}{2057093978843}\right)+780222527176\arctan\left(\frac{1}{2292939666693}\right)-5690712646544\arctan\left(\frac{1}{2423153939240}\right)+59835058644\arctan\left(\frac{2}{6646491492891}\right)+3864092330612\arctan\left(\frac{1}{3419484435037}\right)+7759591570648\arctan\left(\frac{1}{4020467363632}\right)+588452288056\arctan\left(\frac{1}{4398891255452}\right)+81934694504\arctan\left(\frac{1}{5142102426318}\right)-2648518903960\arctan\left(\frac{1}{12091227164593}\right)-1885555745612\arctan\left(\frac{1}{16883072401443}\right)+972842077344\arctan\left(\frac{1}{18104444568932}\right)+5861673409972\arctan\left(\frac{2}{43777069138111}\right)-2279412392016\arctan\left(\frac{1}{27224803284193}\right)-1760725245532\arctan\left(\frac{1}{35527561593282}\right)+1797780298044\arctan\left(\frac{1}{41887379804066}\right)-2749503330296\arctan\left(\frac{1}{45773351286993}\right)-352880732788\arctan\left(\frac{1}{69971515635443}\right)+122979695036\arctan\left(\frac{1}{74305247702057}\right)+714092967640\arctan\left(\frac{1}{79090959114159}\right)+1338653854908\arctan\left(\frac{1}{159493341500663}\right)+4298905189496\arctan\left(\frac{1}{169838669284032}\right)+7026326868780\arctan\left(\frac{1}{229180244713453}\right)-3446219621040\arctan\left(\frac{1}{526264109797943}\right)-3323741795664\arctan\left(\frac{1}{903521917122898}\right)+7459966323124\arctan\left(\frac{1}{1427056404016693}\right)-3700410808336\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	1774431961956[1737653394482] + 2048633606808[2057093978843] + 780222527176[2292939666693] - 5690712646544[2423153939240] + 59835058644[6646491492891/2] + 3864092330612[3419484435037] + 7759591570648[4020467363632] + 588452288056[4398891255452] + 81934694504[5142102426318] - 2648518903960[12091227164593] - 1885555745612[16883072401443] + 972842077344[18104444568932] + 5861673409972[43777069138111/2] - 2279412392016[27224803284193] - 1760725245532[35527561593282] + 1797780298044[41887379804066] - 2749503330296[45773351286993] - 352880732788[69971515635443] + 122979695036[74305247702057] + 714092967640[79090959114159] + 1338653854908[159493341500663] + 4298905189496[169838669284032] + 7026326868780[229180244713453] - 3446219621040[526264109797943] - 3323741795664[903521917122898] + 7459966323124[1427056404016693] - 3700410808336[9505680304081018]
Lehmer's measure	2.00854
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 06 August 2006.] Download references as BibTeΧ