M000000324

$$\pi=3344014720353\arctan\left(\frac{2}{2136194739989}\right)+1826433172593\arctan\left(\frac{1}{1291769674773}\right)+766647361918\arctan\left(\frac{1}{1502963450532}\right)-3608054818945\arctan\left(\frac{1}{2056424542203}\right)-431788240223\arctan\left(\frac{1}{2143501839692}\right)-1073417873326\arctan\left(\frac{2}{4414919775989}\right)-1594326123549\arctan\left(\frac{1}{2292939666693}\right)+1077063636443\arctan\left(\frac{2}{8471235750041}\right)+2748667544468\arctan\left(\frac{1}{5727066010185}\right)+573118690920\arctan\left(\frac{1}{5945958754193}\right)+1462824110406\arctan\left(\frac{1}{7758917519457}\right)+2020580472802\arctan\left(\frac{1}{10546511281730}\right)-10242639936\arctan\left(\frac{2}{28456536638489}\right)+494815311012\arctan\left(\frac{1}{24405694099301}\right)+1524977962880\arctan\left(\frac{1}{41887379804066}\right)-2736475815490\arctan\left(\frac{1}{42859110883727}\right)+1379761551274\arctan\left(\frac{1}{69971515635443}\right)-1162883299368\arctan\left(\frac{1}{94465125845354}\right)+230426377700\arctan\left(\frac{1}{187458398552950}\right)-352335469172\arctan\left(\frac{1}{187530264407868}\right)-19682091896\arctan\left(\frac{1}{211773236092865}\right)+2531114129705\arctan\left(\frac{1}{370392816588001}\right)+2422059960318\arctan\left(\frac{1}{594966589999007}\right)+2576794603238\arctan\left(\frac{1}{758341235653128}\right)-299746594190\arctan\left(\frac{1}{1427056404016693}\right)+1436997395573\arctan\left(\frac{1}{2270451385422943}\right)+416699094873\arctan\left(\frac{1}{4204987898062723}\right)$$

Compact formula	3344014720353[2136194739989/2] + 1826433172593[1291769674773] + 766647361918[1502963450532] - 3608054818945[2056424542203] - 431788240223[2143501839692] - 1073417873326[4414919775989/2] - 1594326123549[2292939666693] + 1077063636443[8471235750041/2] + 2748667544468[5727066010185] + 573118690920[5945958754193] + 1462824110406[7758917519457] + 2020580472802[10546511281730] - 10242639936[28456536638489/2] + 494815311012[24405694099301] + 1524977962880[41887379804066] - 2736475815490[42859110883727] + 1379761551274[69971515635443] - 1162883299368[94465125845354] + 230426377700[187458398552950] - 352335469172[187530264407868] - 19682091896[211773236092865] + 2531114129705[370392816588001] + 2422059960318[594966589999007] + 2576794603238[758341235653128] - 299746594190[1427056404016693] + 1436997395573[2270451385422943] + 416699094873[4204987898062723]
Lehmer's measure	2.01212
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