M000000238

$$\pi=3319338608\arctan\left(\frac{1}{2112819717}\right)+6399903276\arctan\left(\frac{1}{2420845318}\right)-1482442744\arctan\left(\frac{1}{3261365450}\right)+2528122844\arctan\left(\frac{1}{3985944689}\right)-3717178924\arctan\left(\frac{2}{10355370165}\right)-4145206344\arctan\left(\frac{1}{6608082112}\right)+7199026640\arctan\left(\frac{2}{86479075199}\right)-4197708776\arctan\left(\frac{2}{112899039159}\right)-2387777232\arctan\left(\frac{1}{71617196968}\right)+4119512584\arctan\left(\frac{1}{78535779057}\right)-4484249828\arctan\left(\frac{1}{102428655030}\right)+5449176656\arctan\left(\frac{1}{225891903693}\right)+164859944\arctan\left(\frac{1}{283378114193}\right)+1439923688\arctan\left(\frac{1}{324363564309}\right)+678860828\arctan\left(\frac{1}{492806748932}\right)-3921560532\arctan\left(\frac{1}{821345641657}\right)-3037211672\arctan\left(\frac{1}{3737240479718}\right)+577774500\arctan\left(\frac{1}{28148191112477}\right)-2314922648\arctan\left(\frac{1}{69971515635443}\right)-2440282240\arctan\left(\frac{1}{7474541196075273}\right)$$

Compact formula	3319338608[2112819717] + 6399903276[2420845318] - 1482442744[3261365450] + 2528122844[3985944689] - 3717178924[10355370165/2] - 4145206344[6608082112] + 7199026640[86479075199/2] - 4197708776[112899039159/2] - 2387777232[71617196968] + 4119512584[78535779057] - 4484249828[102428655030] + 5449176656[225891903693] + 164859944[283378114193] + 1439923688[324363564309] + 678860828[492806748932] - 3921560532[821345641657] - 3037211672[3737240479718] + 577774500[28148191112477] - 2314922648[69971515635443] - 2440282240[7474541196075273]
Lehmer's measure	1.81045
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 28 March 2004.] Download references as BibTeΧ