M000000328

$$\pi=1797780298044\arctan\left(\frac{1}{1250614473568}\right)+3313292368644\arctan\left(\frac{2}{2554491928011}\right)-2329009631484\arctan\left(\frac{1}{2057093978843}\right)-3244539978328\arctan\left(\frac{1}{2292939666693}\right)+14921882656316\arctan\left(\frac{1}{2423153939240}\right)-9764121914320\arctan\left(\frac{2}{6646491492891}\right)-1858780960220\arctan\left(\frac{1}{3419484435037}\right)-606187106268\arctan\left(\frac{1}{5142102426318}\right)+2770126867892\arctan\left(\frac{1}{8474689723323}\right)-4712884306276\arctan\left(\frac{1}{14483848717682}\right)-2573677546384\arctan\left(\frac{1}{16883072401443}\right)-7429563666452\arctan\left(\frac{1}{18104444568932}\right)-5822542803548\arctan\left(\frac{1}{21856860577557}\right)-3650390831096\arctan\left(\frac{2}{43777069138111}\right)+1041002533560\arctan\left(\frac{1}{27132766222219}\right)-816873161956\arctan\left(\frac{1}{27224803284193}\right)+5836249519972\arctan\left(\frac{1}{35527561593282}\right)+3118347100876\arctan\left(\frac{1}{45773351286993}\right)+3007070154264\arctan\left(\frac{1}{74305247702057}\right)-7571003598636\arctan\left(\frac{1}{79090959114159}\right)-4813421345340\arctan\left(\frac{1}{159493341500663}\right)-5189810715484\arctan\left(\frac{1}{169838669284032}\right)-8637812572536\arctan\left(\frac{1}{229180244713453}\right)-562129161812\arctan\left(\frac{1}{526264109797943}\right)+8650876208132\arctan\left(\frac{1}{903521917122898}\right)-3138408079128\arctan\left(\frac{1}{1427056404016693}\right)-1404772637164\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	1797780298044[1250614473568] + 3313292368644[2554491928011/2] - 2329009631484[2057093978843] - 3244539978328[2292939666693] + 14921882656316[2423153939240] - 9764121914320[6646491492891/2] - 1858780960220[3419484435037] - 606187106268[5142102426318] + 2770126867892[8474689723323] - 4712884306276[14483848717682] - 2573677546384[16883072401443] - 7429563666452[18104444568932] - 5822542803548[21856860577557] - 3650390831096[43777069138111/2] + 1041002533560[27132766222219] - 816873161956[27224803284193] + 5836249519972[35527561593282] + 3118347100876[45773351286993] + 3007070154264[74305247702057] - 7571003598636[79090959114159] - 4813421345340[159493341500663] - 5189810715484[169838669284032] - 8637812572536[229180244713453] - 562129161812[526264109797943] + 8650876208132[903521917122898] - 3138408079128[1427056404016693] - 1404772637164[9505680304081018]
Lehmer's measure	2.01433
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