M000000326

$$\pi=7895452522488\arctan\left(\frac{1}{1116763906292}\right)-4191510957776\arctan\left(\frac{1}{2057093978843}\right)+1224102319940\arctan\left(\frac{1}{2292939666693}\right)-4981338189428\arctan\left(\frac{1}{2401808546428}\right)-1794054451180\arctan\left(\frac{1}{3215723457318}\right)+7788189056312\arctan\left(\frac{1}{4398891255452}\right)-3694323461256\arctan\left(\frac{1}{4807000526307}\right)+1750063334372\arctan\left(\frac{1}{5142102426318}\right)-4449526423532\arctan\left(\frac{1}{7580898173568}\right)-2157927498080\arctan\left(\frac{1}{16883072401443}\right)-2448004753656\arctan\left(\frac{1}{18034841395807}\right)-6395596284052\arctan\left(\frac{1}{19805207795807}\right)+4317586329496\arctan\left(\frac{1}{20651591036669}\right)-1164653458808\arctan\left(\frac{2}{43777069138111}\right)+1925415180756\arctan\left(\frac{1}{27224803284193}\right)+2023310147128\arctan\left(\frac{1}{36384886983307}\right)+352009283768\arctan\left(\frac{1}{38057255532937}\right)-4616101597832\arctan\left(\frac{1}{45773351286993}\right)-5961826971440\arctan\left(\frac{1}{49741306222356}\right)+1636806750680\arctan\left(\frac{1}{68680159040852}\right)+137973554180\arctan\left(\frac{1}{69971515635443}\right)-3559998550012\arctan\left(\frac{1}{74305247702057}\right)-515478535092\arctan\left(\frac{1}{169838669284032}\right)-2643432474152\arctan\left(\frac{1}{526264109797943}\right)-6006482961908\arctan\left(\frac{1}{2471361358083470}\right)-231343098940\arctan\left(\frac{1}{2685728493361068}\right)+1943865889468\arctan\left(\frac{1}{5664961183141174}\right)$$

Compact formula	7895452522488[1116763906292] - 4191510957776[2057093978843] + 1224102319940[2292939666693] - 4981338189428[2401808546428] - 1794054451180[3215723457318] + 7788189056312[4398891255452] - 3694323461256[4807000526307] + 1750063334372[5142102426318] - 4449526423532[7580898173568] - 2157927498080[16883072401443] - 2448004753656[18034841395807] - 6395596284052[19805207795807] + 4317586329496[20651591036669] - 1164653458808[43777069138111/2] + 1925415180756[27224803284193] + 2023310147128[36384886983307] + 352009283768[38057255532937] - 4616101597832[45773351286993] - 5961826971440[49741306222356] + 1636806750680[68680159040852] + 137973554180[69971515635443] - 3559998550012[74305247702057] - 515478535092[169838669284032] - 2643432474152[526264109797943] - 6006482961908[2471361358083470] - 231343098940[2685728493361068] + 1943865889468[5664961183141174]
Lehmer's measure	2.01248
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 13 December 2004.] Download references as BibTeΧ