M000000332

$$\pi=1250027953434\arctan\left(\frac{2}{2056103452041}\right)+301652985140\arctan\left(\frac{1}{1047665713307}\right)+1440314600916\arctan\left(\frac{1}{1259851011582}\right)-262710961780\arctan\left(\frac{1}{1273911086135}\right)+1168007938112\arctan\left(\frac{1}{1921044951457}\right)-1403188085322\arctan\left(\frac{1}{4520110962223}\right)+772210174512\arctan\left(\frac{1}{5142102426318}\right)+468000663384\arctan\left(\frac{1}{5688475754312}\right)+682256062624\arctan\left(\frac{2}{17857722814749}\right)+1224971435828\arctan\left(\frac{1}{15962244871097}\right)-1682130416798\arctan\left(\frac{1}{17545341943072}\right)-196593358822\arctan\left(\frac{1}{18104444568932}\right)+573602623480\arctan\left(\frac{1}{18203022356332}\right)+195767714838\arctan\left(\frac{1}{18758177079442}\right)+350975972080\arctan\left(\frac{2}{43777069138111}\right)+833183174532\arctan\left(\frac{1}{23064526452057}\right)+471568078138\arctan\left(\frac{1}{27224803284193}\right)+702630934916\arctan\left(\frac{1}{55864783210943}\right)-179754911964\arctan\left(\frac{1}{57262110230563}\right)+780615458024\arctan\left(\frac{1}{169838669284032}\right)+37855206384\arctan\left(\frac{1}{180481359172943}\right)+298059172314\arctan\left(\frac{1}{240926005152903}\right)+260375180408\arctan\left(\frac{1}{320714306992682}\right)-1356862272290\arctan\left(\frac{1}{389928169608307}\right)-418362431386\arctan\left(\frac{1}{1516106667217682}\right)+791464332834\arctan\left(\frac{1}{2549868113472987}\right)+49382228570\arctan\left(\frac{1}{4439568777547493}\right)$$

Compact formula	1250027953434[2056103452041/2] + 301652985140[1047665713307] + 1440314600916[1259851011582] - 262710961780[1273911086135] + 1168007938112[1921044951457] - 1403188085322[4520110962223] + 772210174512[5142102426318] + 468000663384[5688475754312] + 682256062624[17857722814749/2] + 1224971435828[15962244871097] - 1682130416798[17545341943072] - 196593358822[18104444568932] + 573602623480[18203022356332] + 195767714838[18758177079442] + 350975972080[43777069138111/2] + 833183174532[23064526452057] + 471568078138[27224803284193] + 702630934916[55864783210943] - 179754911964[57262110230563] + 780615458024[169838669284032] + 37855206384[180481359172943] + 298059172314[240926005152903] + 260375180408[320714306992682] - 1356862272290[389928169608307] - 418362431386[1516106667217682] + 791464332834[2549868113472987] + 49382228570[4439568777547493]
Lehmer's measure	2.01560
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 6 August 2006.] Download references as BibTeΧ