M000000237

$$\pi=3319338608\arctan\left(\frac{1}{2112819717}\right)+3696339592\arctan\left(\frac{1}{2420845318}\right)+2096472596\arctan\left(\frac{2}{5493779561}\right)-569883720\arctan\left(\frac{1}{4474115807}\right)-2936166676\arctan\left(\frac{1}{6608082112}\right)-2734612916\arctan\left(\frac{2}{16758521543}\right)+327559988\arctan\left(\frac{2}{36523075989}\right)+3035558716\arctan\left(\frac{1}{29546599818}\right)+787403960\arctan\left(\frac{1}{38835168211}\right)-3576155960\arctan\left(\frac{1}{42354792693}\right)+5605594024\arctan\left(\frac{2}{86479075199}\right)-759139048\arctan\left(\frac{2}{112899039159}\right)+37177256\arctan\left(\frac{1}{89257170067}\right)+1675052996\arctan\left(\frac{1}{324363564309}\right)-70269364\arctan\left(\frac{1}{579766497643}\right)+985435188\arctan\left(\frac{1}{3737240479718}\right)+1248744548\arctan\left(\frac{1}{11830545643782}\right)-2185314712\arctan\left(\frac{1}{69971515635443}\right)+864244508\arctan\left(\frac{1}{7474541196075273}\right)+1013615240\arctan\left(\frac{1}{24412992821228897}\right)$$

Compact formula	3319338608[2112819717] + 3696339592[2420845318] + 2096472596[5493779561/2] - 569883720[4474115807] - 2936166676[6608082112] - 2734612916[16758521543/2] + 327559988[36523075989/2] + 3035558716[29546599818] + 787403960[38835168211] - 3576155960[42354792693] + 5605594024[86479075199/2] - 759139048[112899039159/2] + 37177256[89257170067] + 1675052996[324363564309] - 70269364[579766497643] + 985435188[3737240479718] + 1248744548[11830545643782] - 2185314712[69971515635443] + 864244508[7474541196075273] + 1013615240[24412992821228897]
Lehmer's measure	1.80998
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