M000000316

$$\pi=3150664561564\arctan\left(\frac{2}{2554491928011}\right)+439187363240\arctan\left(\frac{1}{1688341225737}\right)+846917001394\arctan\left(\frac{1}{2056424542203}\right)-88209363742\arctan\left(\frac{1}{2057093978843}\right)-1529233704278\arctan\left(\frac{1}{2292939666693}\right)+3663043414176\arctan\left(\frac{1}{2423153939240}\right)-4535729068176\arctan\left(\frac{2}{6646491492891}\right)+1650473005416\arctan\left(\frac{1}{3419484435037}\right)-4371935948\arctan\left(\frac{1}{5142102426318}\right)+251287224938\arctan\left(\frac{1}{16883072401443}\right)-1589370196164\arctan\left(\frac{1}{18104444568932}\right)+1587987468872\arctan\left(\frac{2}{43777069138111}\right)-1414855725818\arctan\left(\frac{1}{27224803284193}\right)+2734825534412\arctan\left(\frac{1}{29308445163057}\right)+1811487014468\arctan\left(\frac{1}{35527561593282}\right)+895197499874\arctan\left(\frac{1}{45773351286993}\right)+625125352640\arctan\left(\frac{1}{74305247702057}\right)-2418931929120\arctan\left(\frac{1}{79090959114159}\right)-1372823343416\arctan\left(\frac{1}{159493341500663}\right)-390619778756\arctan\left(\frac{1}{169838669284032}\right)+113652299526\arctan\left(\frac{1}{229180244713453}\right)+425369302958\arctan\left(\frac{1}{339124474237367}\right)+637668572370\arctan\left(\frac{1}{526264109797943}\right)+1859819441194\arctan\left(\frac{1}{903521917122898}\right)+1498155050520\arctan\left(\frac{1}{1427056404016693}\right)-950863296650\arctan\left(\frac{1}{3244023007885213}\right)-2002755201026\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	3150664561564[2554491928011/2] + 439187363240[1688341225737] + 846917001394[2056424542203] - 88209363742[2057093978843] - 1529233704278[2292939666693] + 3663043414176[2423153939240] - 4535729068176[6646491492891/2] + 1650473005416[3419484435037] - 4371935948[5142102426318] + 251287224938[16883072401443] - 1589370196164[18104444568932] + 1587987468872[43777069138111/2] - 1414855725818[27224803284193] + 2734825534412[29308445163057] + 1811487014468[35527561593282] + 895197499874[45773351286993] + 625125352640[74305247702057] - 2418931929120[79090959114159] - 1372823343416[159493341500663] - 390619778756[169838669284032] + 113652299526[229180244713453] + 425369302958[339124474237367] + 637668572370[526264109797943] + 1859819441194[903521917122898] + 1498155050520[1427056404016693] - 950863296650[3244023007885213] - 2002755201026[9505680304081018]
Lehmer's measure	1.99947
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