M000000325

$$\pi=964621941320\arctan\left(\frac{2}{1302521889511}\right)+801544080124\arctan\left(\frac{2}{1957312491989}\right)+1136880689308\arctan\left(\frac{1}{1688341225737}\right)-315209113732\arctan\left(\frac{1}{2056424542203}\right)-882938131728\arctan\left(\frac{1}{2292939666693}\right)+1151484344424\arctan\left(\frac{1}{2423153939240}\right)+1493227383692\arctan\left(\frac{2}{6646491492891}\right)-1572759529576\arctan\left(\frac{1}{3419484435037}\right)+636098238244\arctan\left(\frac{1}{4077098364516}\right)+687877334112\arctan\left(\frac{1}{5142102426318}\right)-442885471352\arctan\left(\frac{1}{18104444568932}\right)-1562677092692\arctan\left(\frac{2}{43777069138111}\right)+1829462255496\arctan\left(\frac{1}{27224803284193}\right)-2035983401896\arctan\left(\frac{1}{29308445163057}\right)+45320993024\arctan\left(\frac{1}{35527561593282}\right)+1627956411436\arctan\left(\frac{1}{36129306114972}\right)-515830542576\arctan\left(\frac{1}{78277699747376}\right)+1247563175020\arctan\left(\frac{1}{79090959114159}\right)+753844357884\arctan\left(\frac{1}{110440936365807}\right)+471354707464\arctan\left(\frac{1}{159493341500663}\right)-1082869048816\arctan\left(\frac{1}{169838669284032}\right)-1874886146912\arctan\left(\frac{1}{229180244713453}\right)-69375793296\arctan\left(\frac{1}{339124474237367}\right)+89779697868\arctan\left(\frac{1}{526264109797943}\right)-954816184976\arctan\left(\frac{1}{1427056404016693}\right)+339981823720\arctan\left(\frac{1}{3244023007885213}\right)-148379815840\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	964621941320[1302521889511/2] + 801544080124[1957312491989/2] + 1136880689308[1688341225737] - 315209113732[2056424542203] - 882938131728[2292939666693] + 1151484344424[2423153939240] + 1493227383692[6646491492891/2] - 1572759529576[3419484435037] + 636098238244[4077098364516] + 687877334112[5142102426318] - 442885471352[18104444568932] - 1562677092692[43777069138111/2] + 1829462255496[27224803284193] - 2035983401896[29308445163057] + 45320993024[35527561593282] + 1627956411436[36129306114972] - 515830542576[78277699747376] + 1247563175020[79090959114159] + 753844357884[110440936365807] + 471354707464[159493341500663] - 1082869048816[169838669284032] - 1874886146912[229180244713453] - 69375793296[339124474237367] + 89779697868[526264109797943] - 954816184976[1427056404016693] + 339981823720[3244023007885213] - 148379815840[9505680304081018]
Lehmer's measure	2.01219
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