M000000318

$$\pi=-1190336267900\arctan\left(\frac{1}{1250614473568}\right)+5848489093256\arctan\left(\frac{2}{2554491928011}\right)+1764812843540\arctan\left(\frac{1}{1688341225737}\right)+218563343184\arctan\left(\frac{1}{2056424542203}\right)-3554853034672\arctan\left(\frac{1}{2292939666693}\right)+3021855167244\arctan\left(\frac{1}{2423153939240}\right)-7396631461064\arctan\left(\frac{2}{6646491492891}\right)+3468656653960\arctan\left(\frac{1}{3419484435037}\right)-1150856660760\arctan\left(\frac{1}{5142102426318}\right)-926214454240\arctan\left(\frac{1}{14483848717682}\right)-1548240681080\arctan\left(\frac{1}{18104444568932}\right)+848117651216\arctan\left(\frac{1}{21856860577557}\right)+3001316035348\arctan\left(\frac{2}{43777069138111}\right)-179140755488\arctan\left(\frac{1}{27132766222219}\right)-2696123385464\arctan\left(\frac{1}{27224803284193}\right)+4348801806676\arctan\left(\frac{1}{29308445163057}\right)+2153705631152\arctan\left(\frac{1}{35527561593282}\right)-1793806576480\arctan\left(\frac{1}{79090959114159}\right)-1375545371420\arctan\left(\frac{1}{159493341500663}\right)-528631019160\arctan\left(\frac{1}{169838669284032}\right)+691697803508\arctan\left(\frac{1}{229180244713453}\right)+130230534932\arctan\left(\frac{1}{339124474237367}\right)+546737180624\arctan\left(\frac{1}{526264109797943}\right)-225714326580\arctan\left(\frac{1}{977167012914932}\right)+4057968341808\arctan\left(\frac{1}{1427056404016693}\right)-2769553222760\arctan\left(\frac{1}{3244023007885213}\right)-3284022860672\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	- 1190336267900[1250614473568] + 5848489093256[2554491928011/2] + 1764812843540[1688341225737] + 218563343184[2056424542203] - 3554853034672[2292939666693] + 3021855167244[2423153939240] - 7396631461064[6646491492891/2] + 3468656653960[3419484435037] - 1150856660760[5142102426318] - 926214454240[14483848717682] - 1548240681080[18104444568932] + 848117651216[21856860577557] + 3001316035348[43777069138111/2] - 179140755488[27132766222219] - 2696123385464[27224803284193] + 4348801806676[29308445163057] + 2153705631152[35527561593282] - 1793806576480[79090959114159] - 1375545371420[159493341500663] - 528631019160[169838669284032] + 691697803508[229180244713453] + 130230534932[339124474237367] + 546737180624[526264109797943] - 225714326580[977167012914932] + 4057968341808[1427056404016693] - 2769553222760[3244023007885213] - 3284022860672[9505680304081018]
Lehmer's measure	2.00527
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 06 August 2006.] Download references as BibTeΧ