M000000323

$$\pi=56309049008\arctan\left(\frac{1}{1708509266693}\right)+3559673210419\arctan\left(\frac{2}{3513625247265}\right)+2130441987787\arctan\left(\frac{1}{2056424542203}\right)+3181416157612\arctan\left(\frac{1}{2142498691247}\right)-728438591393\arctan\left(\frac{1}{2267426627682}\right)-1460151430597\arctan\left(\frac{1}{2821274326057}\right)+1931170986241\arctan\left(\frac{1}{3486467472132}\right)-1066439800553\arctan\left(\frac{2}{7282004207843}\right)+486731317050\arctan\left(\frac{1}{5584843622493}\right)-1945783134820\arctan\left(\frac{1}{5602034310634}\right)-1566672008906\arctan\left(\frac{1}{5740631503932}\right)-305857070674\arctan\left(\frac{1}{11244667034168}\right)-206700262005\arctan\left(\frac{1}{12575227775843}\right)-120543390603\arctan\left(\frac{1}{13474294213307}\right)-829338460356\arctan\left(\frac{1}{15962244871097}\right)-692357653063\arctan\left(\frac{1}{18203022356332}\right)-2645550113711\arctan\left(\frac{1}{30149632444007}\right)-1261171853714\arctan\left(\frac{1}{37179598561432}\right)-1033943947142\arctan\left(\frac{1}{46150510628682}\right)-2763240139064\arctan\left(\frac{1}{69971515635443}\right)-543782818579\arctan\left(\frac{1}{114248631197147}\right)+917868424535\arctan\left(\frac{1}{406730714577182}\right)+676438892916\arctan\left(\frac{1}{686308367425978}\right)+864231009861\arctan\left(\frac{1}{1516106667217682}\right)-2402791499168\arctan\left(\frac{1}{4439568777547493}\right)+1166443667120\arctan\left(\frac{1}{39840505668541817}\right)+1172074102579\arctan\left(\frac{1}{74295753693510382}\right)$$

Compact formula	56309049008[1708509266693] + 3559673210419[3513625247265/2] + 2130441987787[2056424542203] + 3181416157612[2142498691247] - 728438591393[2267426627682] - 1460151430597[2821274326057] + 1931170986241[3486467472132] - 1066439800553[7282004207843/2] + 486731317050[5584843622493] - 1945783134820[5602034310634] - 1566672008906[5740631503932] - 305857070674[11244667034168] - 206700262005[12575227775843] - 120543390603[13474294213307] - 829338460356[15962244871097] - 692357653063[18203022356332] - 2645550113711[30149632444007] - 1261171853714[37179598561432] - 1033943947142[46150510628682] - 2763240139064[69971515635443] - 543782818579[114248631197147] + 917868424535[406730714577182] + 676438892916[686308367425978] + 864231009861[1516106667217682] - 2402791499168[4439568777547493] + 1166443667120[39840505668541817] + 1172074102579[74295753693510382]
Lehmer's measure	2.01143
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