M000000330

$$\pi=945394895862\arctan\left(\frac{2}{1302521889511}\right)-240584778038\arctan\left(\frac{2}{1413806957179}\right)+2032656404798\arctan\left(\frac{2}{2554491928011}\right)+140204150280\arctan\left(\frac{1}{2057093978843}\right)-792965861368\arctan\left(\frac{1}{2292939666693}\right)+3525709482880\arctan\left(\frac{1}{2423153939240}\right)-2677631463978\arctan\left(\frac{2}{6646491492891}\right)+274240405808\arctan\left(\frac{1}{3419484435037}\right)+322519472542\arctan\left(\frac{1}{5142102426318}\right)-922521184946\arctan\left(\frac{1}{16883072401443}\right)-1193811822026\arctan\left(\frac{1}{18104444568932}\right)+229394534068\arctan\left(\frac{2}{43777069138111}\right)-593928048722\arctan\left(\frac{1}{27224803284193}\right)+1106676896644\arctan\left(\frac{1}{35527561593282}\right)-94656289946\arctan\left(\frac{1}{36129306114972}\right)+1673447535620\arctan\left(\frac{1}{45773351286993}\right)+1322537158722\arctan\left(\frac{1}{74305247702057}\right)+129935619554\arctan\left(\frac{1}{78277699747376}\right)-1190274613870\arctan\left(\frac{1}{79090959114159}\right)-112295954750\arctan\left(\frac{1}{110440936365807}\right)-1416452332518\arctan\left(\frac{1}{159493341500663}\right)-717511187246\arctan\left(\frac{1}{169838669284032}\right)-638608411922\arctan\left(\frac{1}{229180244713453}\right)+1106666864430\arctan\left(\frac{1}{526264109797943}\right)+1692674581078\arctan\left(\frac{1}{903521917122898}\right)-299625247524\arctan\left(\frac{1}{1427056404016693}\right)-1069531569180\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	945394895862[1302521889511/2] - 240584778038[1413806957179/2] + 2032656404798[2554491928011/2] + 140204150280[2057093978843] - 792965861368[2292939666693] + 3525709482880[2423153939240] - 2677631463978[6646491492891/2] + 274240405808[3419484435037] + 322519472542[5142102426318] - 922521184946[16883072401443] - 1193811822026[18104444568932] + 229394534068[43777069138111/2] - 593928048722[27224803284193] + 1106676896644[35527561593282] - 94656289946[36129306114972] + 1673447535620[45773351286993] + 1322537158722[74305247702057] + 129935619554[78277699747376] - 1190274613870[79090959114159] - 112295954750[110440936365807] - 1416452332518[159493341500663] - 717511187246[169838669284032] - 638608411922[229180244713453] + 1106666864430[526264109797943] + 1692674581078[903521917122898] - 299625247524[1427056404016693] - 1069531569180[9505680304081018]
Lehmer's measure	2.01491
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