M000000333

$$\pi=1245798198656\arctan\left(\frac{2}{1588906191929}\right)+827706299200\arctan\left(\frac{1}{1107182624153}\right)+4501865232432\arctan\left(\frac{1}{1131133876777}\right)-2435771305468\arctan\left(\frac{2}{2276161346189}\right)+2379382346432\arctan\left(\frac{1}{2056424542203}\right)-1728214344028\arctan\left(\frac{1}{2292939666693}\right)-3969772940996\arctan\left(\frac{1}{2554104718836}\right)+1699605407892\arctan\left(\frac{1}{5426436245407}\right)+481003349268\arctan\left(\frac{1}{5727066010185}\right)-599183775420\arctan\left(\frac{1}{5945958754193}\right)-254714354096\arctan\left(\frac{1}{7758917519457}\right)-3987183512\arctan\left(\frac{1}{10209548813937}\right)+731376547692\arctan\left(\frac{1}{11244667034168}\right)-1401549708640\arctan\left(\frac{1}{15962244871097}\right)+188279316556\arctan\left(\frac{1}{33308851938318}\right)-3770502840512\arctan\left(\frac{1}{41887379804066}\right)-375053893652\arctan\left(\frac{1}{69971515635443}\right)-13171285492\arctan\left(\frac{1}{158682175700807}\right)-2115002027944\arctan\left(\frac{1}{187458398552950}\right)-1184928170484\arctan\left(\frac{1}{211773236092865}\right)-7056387752\arctan\left(\frac{1}{258213230677943}\right)+206579011264\arctan\left(\frac{1}{370392816588001}\right)+491886665456\arctan\left(\frac{1}{463881089866359}\right)+866312526488\arctan\left(\frac{1}{758341235653128}\right)-87967450552\arctan\left(\frac{1}{1427056404016693}\right)+1488753909024\arctan\left(\frac{1}{2270451385422943}\right)+117603984760\arctan\left(\frac{1}{4204987898062723}\right)$$

Compact formula	1245798198656[1588906191929/2] + 827706299200[1107182624153] + 4501865232432[1131133876777] - 2435771305468[2276161346189/2] + 2379382346432[2056424542203] - 1728214344028[2292939666693] - 3969772940996[2554104718836] + 1699605407892[5426436245407] + 481003349268[5727066010185] - 599183775420[5945958754193] - 254714354096[7758917519457] - 3987183512[10209548813937] + 731376547692[11244667034168] - 1401549708640[15962244871097] + 188279316556[33308851938318] - 3770502840512[41887379804066] - 375053893652[69971515635443] - 13171285492[158682175700807] - 2115002027944[187458398552950] - 1184928170484[211773236092865] - 7056387752[258213230677943] + 206579011264[370392816588001] + 491886665456[463881089866359] + 866312526488[758341235653128] - 87967450552[1427056404016693] + 1488753909024[2270451385422943] + 117603984760[4204987898062723]
Lehmer's measure	2.01609
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