M000000346

$$\pi=-12776653512188\arctan\left(\frac{2}{19216305209891}\right)-12851426601368\arctan\left(\frac{1}{12575227775843}\right)+1818361152412\arctan\left(\frac{1}{13474294213307}\right)+13543733674556\arctan\left(\frac{1}{15962244871097}\right)+17507516124364\arctan\left(\frac{1}{18104444568932}\right)+27415374741520\arctan\left(\frac{1}{18203022356332}\right)+7117377724708\arctan\left(\frac{1}{18758177079442}\right)+12146098232304\arctan\left(\frac{2}{43777069138111}\right)+11022179610456\arctan\left(\frac{1}{23064526452057}\right)+38655307314992\arctan\left(\frac{1}{27224803284193}\right)+24427192088744\arctan\left(\frac{1}{30027152008147}\right)-3858370957824\arctan\left(\frac{1}{37179598561432}\right)-19960179010236\arctan\left(\frac{1}{38057255532937}\right)-24647681594504\arctan\left(\frac{1}{46150510628682}\right)-1807543615084\arctan\left(\frac{1}{52069489979033}\right)-11199819554844\arctan\left(\frac{1}{53082257312807}\right)+11350404952836\arctan\left(\frac{1}{57262110230563}\right)+11272979769324\arctan\left(\frac{1}{69971515635443}\right)-24679793233292\arctan\left(\frac{1}{79507238248932}\right)-10259618715868\arctan\left(\frac{1}{169838669284032}\right)-47783031627888\arctan\left(\frac{1}{180481359172943}\right)-7978363915356\arctan\left(\frac{1}{240926005152903}\right)+28074616116504\arctan\left(\frac{1}{295684706259317}\right)+3731775692648\arctan\left(\frac{1}{389928169608307}\right)+4932263588660\arctan\left(\frac{1}{1516106667217682}\right)+3855456707164\arctan\left(\frac{1}{1900216428167270}\right)-23165197400992\arctan\left(\frac{1}{2549868113472987}\right)+36086193256716\arctan\left(\frac{1}{4439568777547493}\right)-19225051870224\arctan\left(\frac{1}{74295753693510382}\right)$$

Compact formula	- 12776653512188[19216305209891/2] - 12851426601368[12575227775843] + 1818361152412[13474294213307] + 13543733674556[15962244871097] + 17507516124364[18104444568932] + 27415374741520[18203022356332] + 7117377724708[18758177079442] + 12146098232304[43777069138111/2] + 11022179610456[23064526452057] + 38655307314992[27224803284193] + 24427192088744[30027152008147] - 3858370957824[37179598561432] - 19960179010236[38057255532937] - 24647681594504[46150510628682] - 1807543615084[52069489979033] - 11199819554844[53082257312807] + 11350404952836[57262110230563] + 11272979769324[69971515635443] - 24679793233292[79507238248932] - 10259618715868[169838669284032] - 47783031627888[180481359172943] - 7978363915356[240926005152903] + 28074616116504[295684706259317] + 3731775692648[389928169608307] + 4932263588660[1516106667217682] + 3855456707164[1900216428167270] - 23165197400992[2549868113472987] + 36086193256716[4439568777547493] - 19225051870224[74295753693510382]
Lehmer's measure	2.08000
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 4 August 2006.] Download references as BibTeΧ