M000000329

$$\pi=-819853465580\arctan\left(\frac{1}{1921044951457}\right)+894820123180\arctan\left(\frac{1}{2401808546428}\right)+2784799977872\arctan\left(\frac{2}{5345202735279}\right)-53356070168\arctan\left(\frac{1}{3621667588383}\right)+1980257317428\arctan\left(\frac{1}{4749927118057}\right)+1155078421316\arctan\left(\frac{1}{5142102426318}\right)+3433269650788\arctan\left(\frac{1}{5602034310634}\right)+2402451550204\arctan\left(\frac{1}{5688475754312}\right)-794950598056\arctan\left(\frac{1}{6202471697443}\right)+566843940348\arctan\left(\frac{1}{7580898173568}\right)+3713370830808\arctan\left(\frac{1}{8283978614930}\right)-1208311485536\arctan\left(\frac{1}{9339643670807}\right)+2874772134572\arctan\left(\frac{1}{15962244871097}\right)+473260397776\arctan\left(\frac{1}{18104444568932}\right)+3418771972448\arctan\left(\frac{1}{18203022356332}\right)-2339426810876\arctan\left(\frac{1}{20519945126283}\right)-360703615320\arctan\left(\frac{1}{23064526452057}\right)-18030796196\arctan\left(\frac{2}{74963671338441}\right)-914329902624\arctan\left(\frac{1}{38057255532937}\right)+317812781940\arctan\left(\frac{1}{69971515635443}\right)-601998188040\arctan\left(\frac{2}{156235501440983}\right)-261926779360\arctan\left(\frac{1}{180481359172943}\right)-1898784967612\arctan\left(\frac{1}{240926005152903}\right)-764734035248\arctan\left(\frac{1}{389928169608307}\right)+649255921460\arctan\left(\frac{1}{2549868113472987}\right)+2426266075232\arctan\left(\frac{1}{4439568777547493}\right)+781804438600\arctan\left(\frac{1}{8489727499760268}\right)$$

Compact formula	- 819853465580[1921044951457] + 894820123180[2401808546428] + 2784799977872[5345202735279/2] - 53356070168[3621667588383] + 1980257317428[4749927118057] + 1155078421316[5142102426318] + 3433269650788[5602034310634] + 2402451550204[5688475754312] - 794950598056[6202471697443] + 566843940348[7580898173568] + 3713370830808[8283978614930] - 1208311485536[9339643670807] + 2874772134572[15962244871097] + 473260397776[18104444568932] + 3418771972448[18203022356332] - 2339426810876[20519945126283] - 360703615320[23064526452057] - 18030796196[74963671338441/2] - 914329902624[38057255532937] + 317812781940[69971515635443] - 601998188040[156235501440983/2] - 261926779360[180481359172943] - 1898784967612[240926005152903] - 764734035248[389928169608307] + 649255921460[2549868113472987] + 2426266075232[4439568777547493] + 781804438600[8489727499760268]
Lehmer's measure	2.01485
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 16 September 2010.] Download references as BibTeΧ