M000000214

$$\pi=-359896564\arctan\left(\frac{1}{213625056}\right)+553991136\arctan\left(\frac{1}{286624818}\right)+302816252\arctan\left(\frac{1}{287100705}\right)+737984700\arctan\left(\frac{2}{638252189}\right)-662065656\arctan\left(\frac{1}{1454097393}\right)-40621960\arctan\left(\frac{1}{1479406293}\right)+27200072\arctan\left(\frac{2}{7850392761}\right)+180325392\arctan\left(\frac{1}{4038832337}\right)-269375792\arctan\left(\frac{1}{6608082112}\right)-132173580\arctan\left(\frac{1}{18710140581}\right)-162509108\arctan\left(\frac{1}{29546599818}\right)+432136520\arctan\left(\frac{2}{112899039159}\right)+562135920\arctan\left(\frac{1}{225891903693}\right)+439521688\arctan\left(\frac{1}{265542904947}\right)-365807620\arctan\left(\frac{1}{378137211957}\right)-267706128\arctan\left(\frac{1}{3737240479718}\right)+25156512\arctan\left(\frac{1}{11830545643782}\right)-102526176\arctan\left(\frac{1}{28148191112477}\right)$$

Compact formula	`- 359896564[213625056] + 553991136[286624818] + 302816252[287100705] + 737984700[638252189/2] - 662065656[1454097393] - 40621960[1479406293] + 27200072[7850392761/2] + 180325392[4038832337] - 269375792[6608082112] - 132173580[18710140581] - 162509108[29546599818] + 432136520[112899039159/2] + 562135920[225891903693] + 439521688[265542904947] - 365807620[378137211957] - 267706128[3737240479718] + 25156512[11830545643782] - 102526176[28148191112477]`
Lehmer's measure	1.78070
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 11 August 2006.] Download references as BibTeΧ