M000000236

$$\pi=1488450788\arctan\left(\frac{2}{3472598789}\right)+2069272524\arctan\left(\frac{2}{4074292887}\right)+1830887820\arctan\left(\frac{1}{4038832337}\right)+5028624338\arctan\left(\frac{2}{12800795261}\right)-131706546\arctan\left(\frac{1}{6608082112}\right)-2248139894\arctan\left(\frac{1}{18710140581}\right)-27200072\arctan\left(\frac{1}{24139206772}\right)+1528675280\arctan\left(\frac{1}{29546599818}\right)+4879569650\arctan\left(\frac{2}{112899039159}\right)+1561876482\arctan\left(\frac{1}{71354040503}\right)-1197156014\arctan\left(\frac{1}{225891903693}\right)+5427524066\arctan\left(\frac{1}{265542904947}\right)-1743789234\arctan\left(\frac{1}{378137211957}\right)+1621337174\arctan\left(\frac{1}{1053586529897}\right)-4147553548\arctan\left(\frac{1}{2554104718836}\right)-2839961306\arctan\left(\frac{1}{3737240479718}\right)+3193698874\arctan\left(\frac{1}{3931260155877}\right)-1293364410\arctan\left(\frac{1}{11830545643782}\right)+3593562412\arctan\left(\frac{1}{12433164124467}\right)+1229416634\arctan\left(\frac{1}{28148191112477}\right)$$

Compact formula	1488450788[3472598789/2] + 2069272524[4074292887/2] + 1830887820[4038832337] + 5028624338[12800795261/2] - 131706546[6608082112] - 2248139894[18710140581] - 27200072[24139206772] + 1528675280[29546599818] + 4879569650[112899039159/2] + 1561876482[71354040503] - 1197156014[225891903693] + 5427524066[265542904947] - 1743789234[378137211957] + 1621337174[1053586529897] - 4147553548[2554104718836] - 2839961306[3737240479718] + 3193698874[3931260155877] - 1293364410[11830545643782] + 3593562412[12433164124467] + 1229416634[28148191112477]
Lehmer's measure	1.80978
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 22 February 2004.] Download references as BibTeΧ