M000000313

$$\pi=2585495736876\arctan\left(\frac{2}{2276161346189}\right)+3865383445616\arctan\left(\frac{1}{2056424542203}\right)-3049555058672\arctan\left(\frac{1}{2267426627682}\right)-4171365642860\arctan\left(\frac{1}{3486467472132}\right)+4440176407812\arctan\left(\frac{2}{7282004207843}\right)-1403902631888\arctan\left(\frac{1}{5584843622493}\right)+54797277800\arctan\left(\frac{1}{5602034310634}\right)+1021495362304\arctan\left(\frac{1}{5740631503932}\right)+1348350942876\arctan\left(\frac{2}{19216305209891}\right)+988856457528\arctan\left(\frac{1}{11244667034168}\right)-7614955515788\arctan\left(\frac{1}{12575227775843}\right)+2145675976808\arctan\left(\frac{1}{13474294213307}\right)+6302272742156\arctan\left(\frac{1}{15962244871097}\right)+6063668130976\arctan\left(\frac{1}{18203022356332}\right)+914123096708\arctan\left(\frac{1}{30149632444007}\right)-1371118317396\arctan\left(\frac{1}{37179598561432}\right)-1200199459832\arctan\left(\frac{1}{46150510628682}\right)-5783260259636\arctan\left(\frac{1}{53082257312807}\right)-2178324814808\arctan\left(\frac{1}{69971515635443}\right)+1836996534264\arctan\left(\frac{2}{175614682377261}\right)-223246763920\arctan\left(\frac{1}{114248631197147}\right)+3294034255628\arctan\left(\frac{1}{169838669284032}\right)+2000580412620\arctan\left(\frac{1}{295684706259317}\right)-5106821366720\arctan\left(\frac{1}{686308367425978}\right)+4032698230212\arctan\left(\frac{1}{4439568777547493}\right)-6453813126780\arctan\left(\frac{1}{39840505668541817}\right)-1094145264832\arctan\left(\frac{1}{74295753693510382}\right)$$

Compact formula	2585495736876[2276161346189/2] + 3865383445616[2056424542203] - 3049555058672[2267426627682] - 4171365642860[3486467472132] + 4440176407812[7282004207843/2] - 1403902631888[5584843622493] + 54797277800[5602034310634] + 1021495362304[5740631503932] + 1348350942876[19216305209891/2] + 988856457528[11244667034168] - 7614955515788[12575227775843] + 2145675976808[13474294213307] + 6302272742156[15962244871097] + 6063668130976[18203022356332] + 914123096708[30149632444007] - 1371118317396[37179598561432] - 1200199459832[46150510628682] - 5783260259636[53082257312807] - 2178324814808[69971515635443] + 1836996534264[175614682377261/2] - 223246763920[114248631197147] + 3294034255628[169838669284032] + 2000580412620[295684706259317] - 5106821366720[686308367425978] + 4032698230212[4439568777547493] - 6453813126780[39840505668541817] - 1094145264832[74295753693510382]
Lehmer's measure	1.99621
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