M000000286

$$\pi=224648447456\arctan\left(\frac{1}{138873731225}\right)+177654726720\arctan\left(\frac{1}{148431551771}\right)-134237498118\arctan\left(\frac{1}{168722145007}\right)+125736081286\arctan\left(\frac{1}{202954204459}\right)-42080107266\arctan\left(\frac{1}{218123852367}\right)-86246172578\arctan\left(\frac{1}{250645741818}\right)+94069213216\arctan\left(\frac{1}{261002206018}\right)+99642962706\arctan\left(\frac{1}{269007136889}\right)+85503479620\arctan\left(\frac{1}{548275361132}\right)+74409349014\arctan\left(\frac{1}{656902304557}\right)+91529556198\arctan\left(\frac{1}{1372432573478}\right)-30306300746\arctan\left(\frac{1}{3761284561432}\right)-18054250312\arctan\left(\frac{1}{5745192731179}\right)-17828968844\arctan\left(\frac{2}{13078246979509}\right)+66241836426\arctan\left(\frac{1}{8589803519307}\right)-135821729862\arctan\left(\frac{1}{10892900268195}\right)-78290787002\arctan\left(\frac{1}{17780261434697}\right)-113876870462\arctan\left(\frac{1}{25331597869589}\right)+29570125506\arctan\left(\frac{1}{38759264489343}\right)+52405391548\arctan\left(\frac{1}{165171481279982}\right)+73041191872\arctan\left(\frac{1}{169838669284032}\right)-80691245808\arctan\left(\frac{1}{342036110675693}\right)-160094285298\arctan\left(\frac{1}{772654028018543}\right)-115991851386\arctan\left(\frac{1}{1948025182233307}\right)$$

Compact formula	224648447456[138873731225] + 177654726720[148431551771] - 134237498118[168722145007] + 125736081286[202954204459] - 42080107266[218123852367] - 86246172578[250645741818] + 94069213216[261002206018] + 99642962706[269007136889] + 85503479620[548275361132] + 74409349014[656902304557] + 91529556198[1372432573478] - 30306300746[3761284561432] - 18054250312[5745192731179] - 17828968844[13078246979509/2] + 66241836426[8589803519307] - 135821729862[10892900268195] - 78290787002[17780261434697] - 113876870462[25331597869589] + 29570125506[38759264489343] + 52405391548[165171481279982] + 73041191872[169838669284032] - 80691245808[342036110675693] - 160094285298[772654028018543] - 115991851386[1948025182233307]
Lehmer's measure	1.91556
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 23 January 2005.] Download references as BibTeΧ