M000000245

$$\pi=-1843772048\arctan\left(\frac{1}{2112819717}\right)+4012126044\arctan\left(\frac{1}{2420845318}\right)+2234736180\arctan\left(\frac{2}{4895309741}\right)+226473660\arctan\left(\frac{2}{7850392761}\right)+7581289880\arctan\left(\frac{1}{3985944689}\right)-5591138076\arctan\left(\frac{1}{6608082112}\right)+1598972784\arctan\left(\frac{1}{9396687283}\right)+5703707900\arctan\left(\frac{1}{29777042712}\right)+706514292\arctan\left(\frac{2}{86479075199}\right)-1809931544\arctan\left(\frac{2}{112899039159}\right)+964926828\arctan\left(\frac{1}{225891903693}\right)-2763514532\arctan\left(\frac{1}{283378114193}\right)+905334488\arctan\left(\frac{2}{632886751489}\right)-3723186968\arctan\left(\frac{1}{324363564309}\right)-540597244\arctan\left(\frac{1}{573904314793}\right)+562689296\arctan\left(\frac{1}{821345641657}\right)-4256669744\arctan\left(\frac{1}{3737240479718}\right)-5125933400\arctan\left(\frac{1}{28148191112477}\right)+613451828\arctan\left(\frac{1}{69971515635443}\right)-6661547396\arctan\left(\frac{1}{7474541196075273}\right)$$

Compact formula	- 1843772048[2112819717] + 4012126044[2420845318] + 2234736180[4895309741/2] + 226473660[7850392761/2] + 7581289880[3985944689] - 5591138076[6608082112] + 1598972784[9396687283] + 5703707900[29777042712] + 706514292[86479075199/2] - 1809931544[112899039159/2] + 964926828[225891903693] - 2763514532[283378114193] + 905334488[632886751489/2] - 3723186968[324363564309] - 540597244[573904314793] + 562689296[821345641657] - 4256669744[3737240479718] - 5125933400[28148191112477] + 613451828[69971515635443] - 6661547396[7474541196075273]
Lehmer's measure	1.82063
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 10 August 2006.] Download references as BibTeΧ