M000000363

$$\pi=-472355675494016\arctan\left(\frac{1}{12575227775843}\right)-70391859458532\arctan\left(\frac{1}{13474294213307}\right)-15852482045700\arctan\left(\frac{1}{15962244871097}\right)+648620192990580\arctan\left(\frac{1}{18203022356332}\right)+298820368802828\arctan\left(\frac{1}{18758177079442}\right)-473192352425744\arctan\left(\frac{1}{19315514384367}\right)+322091078508980\arctan\left(\frac{2}{43777069138111}\right)+71354473655004\arctan\left(\frac{1}{24583813961543}\right)-63531816126012\arctan\left(\frac{1}{37179598561432}\right)+196751885695192\arctan\left(\frac{1}{38057255532937}\right)+20793095858116\arctan\left(\frac{1}{46150510628682}\right)+178927627777584\arctan\left(\frac{1}{52069489979033}\right)-243066828643272\arctan\left(\frac{1}{53082257312807}\right)+19089223763988\arctan\left(\frac{1}{69971515635443}\right)-217645834050800\arctan\left(\frac{2}{175614682377261}\right)+52619762068112\arctan\left(\frac{1}{169838669284032}\right)-224982378629316\arctan\left(\frac{1}{180481359172943}\right)+464027618020468\arctan\left(\frac{1}{240926005152903}\right)+260373805739896\arctan\left(\frac{1}{295684706259317}\right)+43514871868640\arctan\left(\frac{1}{389928169608307}\right)-289617893642408\arctan\left(\frac{1}{686308367425978}\right)-162994771004520\arctan\left(\frac{1}{1280491925873282}\right)+272680824911252\arctan\left(\frac{1}{1516106667217682}\right)-193689959050764\arctan\left(\frac{1}{1900216428167270}\right)+310115450070664\arctan\left(\frac{1}{4184847325111003}\right)+536888134157656\arctan\left(\frac{1}{4439568777547493}\right)-194339480142136\arctan\left(\frac{1}{24412992821228897}\right)-507252235015268\arctan\left(\frac{1}{38716856599806432}\right)-373917107522076\arctan\left(\frac{1}{39840505668541817}\right)+98425946193340\arctan\left(\frac{1}{74295753693510382}\right)$$

Compact formula	- 472355675494016[12575227775843] - 70391859458532[13474294213307] - 15852482045700[15962244871097] + 648620192990580[18203022356332] + 298820368802828[18758177079442] - 473192352425744[19315514384367] + 322091078508980[43777069138111/2] + 71354473655004[24583813961543] - 63531816126012[37179598561432] + 196751885695192[38057255532937] + 20793095858116[46150510628682] + 178927627777584[52069489979033] - 243066828643272[53082257312807] + 19089223763988[69971515635443] - 217645834050800[175614682377261/2] + 52619762068112[169838669284032] - 224982378629316[180481359172943] + 464027618020468[240926005152903] + 260373805739896[295684706259317] + 43514871868640[389928169608307] - 289617893642408[686308367425978] - 162994771004520[1280491925873282] + 272680824911252[1516106667217682] - 193689959050764[1900216428167270] + 310115450070664[4184847325111003] + 536888134157656[4439568777547493] - 194339480142136[24412992821228897] - 507252235015268[38716856599806432] - 373917107522076[39840505668541817] + 98425946193340[74295753693510382]
Lehmer's measure	2.09537
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 Amrik Singh Nimbran on 17 June 2011.] Download references as BibTeΧ