M000000209

$$\pi=-102958034\arctan\left(\frac{1}{213625056}\right)+576929997\arctan\left(\frac{2}{497992127}\right)+382781205\arctan\left(\frac{1}{590268258}\right)+602465298\arctan\left(\frac{1}{1454097393}\right)+264575430\arctan\left(\frac{1}{1479406293}\right)+22938861\arctan\left(\frac{1}{3816349818}\right)-106194348\arctan\left(\frac{1}{4038832337}\right)+414341592\arctan\left(\frac{1}{6608082112}\right)+148081449\arctan\left(\frac{1}{18710140581}\right)+702395034\arctan\left(\frac{1}{24858161060}\right)-265035284\arctan\left(\frac{1}{29546599818}\right)-149054688\arctan\left(\frac{2}{112899039159}\right)+455726171\arctan\left(\frac{1}{102416588812}\right)-476784959\arctan\left(\frac{1}{113201494333}\right)-645276913\arctan\left(\frac{1}{265542904947}\right)+35273597\arctan\left(\frac{1}{378137211957}\right)-87973775\arctan\left(\frac{1}{3737240479718}\right)+227827726\arctan\left(\frac{1}{11830545643782}\right)$$

Compact formula	`- 102958034[213625056] + 576929997[497992127/2] + 382781205[590268258] + 602465298[1454097393] + 264575430[1479406293] + 22938861[3816349818] - 106194348[4038832337] + 414341592[6608082112] + 148081449[18710140581] + 702395034[24858161060] - 265035284[29546599818] - 149054688[112899039159/2] + 455726171[102416588812] - 476784959[113201494333] - 645276913[265542904947] + 35273597[378137211957] - 87973775[3737240479718] + 227827726[11830545643782]`
Lehmer's measure	1.77494
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 January 2004.] Download references as BibTeΧ