M000000353

$$\pi=5789884254544\arctan\left(\frac{1}{12575227775843}\right)+86571939559716\arctan\left(\frac{1}{13474294213307}\right)+48906737702960\arctan\left(\frac{1}{15962244871097}\right)+51506220379388\arctan\left(\frac{1}{18104444568932}\right)-121301044647488\arctan\left(\frac{1}{18203022356332}\right)-24628523808396\arctan\left(\frac{1}{23064526452057}\right)+47197653158940\arctan\left(\frac{1}{24583813961543}\right)+34520314187412\arctan\left(\frac{1}{30027152008147}\right)-1020263678884\arctan\left(\frac{1}{37179598561432}\right)-132240270006836\arctan\left(\frac{1}{38057255532937}\right)-6531591575388\arctan\left(\frac{1}{46150510628682}\right)-115324653773332\arctan\left(\frac{1}{52069489979033}\right)+83330370941692\arctan\left(\frac{1}{57262110230563}\right)+33825957193368\arctan\left(\frac{1}{69971515635443}\right)-156988511468068\arctan\left(\frac{1}{79507238248932}\right)+113695196460804\arctan\left(\frac{1}{89934915848057}\right)-90540995562344\arctan\left(\frac{1}{180481359172943}\right)+1957141224152\arctan\left(\frac{1}{240926005152903}\right)+2591705144300\arctan\left(\frac{1}{389928169608307}\right)+106259054244780\arctan\left(\frac{1}{686308367425978}\right)-20666497907608\arctan\left(\frac{1}{1280491925873282}\right)+2415228792340\arctan\left(\frac{1}{1516106667217682}\right)+66708559138952\arctan\left(\frac{1}{1900216428167270}\right)-37907741088552\arctan\left(\frac{1}{2549868113472987}\right)-177178854172476\arctan\left(\frac{1}{4184847325111003}\right)+12433833766044\arctan\left(\frac{1}{4439568777547493}\right)+75950828426596\arctan\left(\frac{1}{24412992821228897}\right)+96504676501568\arctan\left(\frac{1}{38716856599806432}\right)+44884766716796\arctan\left(\frac{1}{39840505668541817}\right)-85862540258412\arctan\left(\frac{1}{74295753693510382}\right)$$

Compact formula	5789884254544[12575227775843] + 86571939559716[13474294213307] + 48906737702960[15962244871097] + 51506220379388[18104444568932] - 121301044647488[18203022356332] - 24628523808396[23064526452057] + 47197653158940[24583813961543] + 34520314187412[30027152008147] - 1020263678884[37179598561432] - 132240270006836[38057255532937] - 6531591575388[46150510628682] - 115324653773332[52069489979033] + 83330370941692[57262110230563] + 33825957193368[69971515635443] - 156988511468068[79507238248932] + 113695196460804[89934915848057] - 90540995562344[180481359172943] + 1957141224152[240926005152903] + 2591705144300[389928169608307] + 106259054244780[686308367425978] - 20666497907608[1280491925873282] + 2415228792340[1516106667217682] + 66708559138952[1900216428167270] - 37907741088552[2549868113472987] - 177178854172476[4184847325111003] + 12433833766044[4439568777547493] + 75950828426596[24412992821228897] + 96504676501568[38716856599806432] + 44884766716796[39840505668541817] - 85862540258412[74295753693510382]
Lehmer's measure	2.09150
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 3 July 2005.] Download references as BibTeΧ