M000000178

$$\pi=89898168\arctan\left(\frac{1}{82189674}\right)+115983700\arctan\left(\frac{1}{133311327}\right)+25725960\arctan\left(\frac{1}{152087733}\right)+112176128\arctan\left(\frac{1}{227661182}\right)+187937912\arctan\left(\frac{1}{244653118}\right)-53948548\arctan\left(\frac{1}{284862638}\right)-31992188\arctan\left(\frac{1}{355671793}\right)-45985944\arctan\left(\frac{1}{403478642}\right)+81231144\arctan\left(\frac{1}{403916362}\right)-42342444\arctan\left(\frac{1}{727507932}\right)-62632540\arctan\left(\frac{1}{15234751332}\right)+81743564\arctan\left(\frac{2}{74522099649}\right)+6107352\arctan\left(\frac{1}{106334643058}\right)-29427040\arctan\left(\frac{1}{134520516108}\right)+27077796\arctan\left(\frac{1}{138873731225}\right)-28429632\arctan\left(\frac{1}{169838669284032}\right)$$

Compact formula	`89898168[82189674] + 115983700[133311327] + 25725960[152087733] + 112176128[227661182] + 187937912[244653118] - 53948548[284862638] - 31992188[355671793] - 45985944[403478642] + 81231144[403916362] - 42342444[727507932] - 62632540[15234751332] + 81743564[74522099649/2] + 6107352[106334643058] - 29427040[134520516108] + 27077796[138873731225] - 28429632[169838669284032]`
Lehmer's measure	1.72433
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 16 December 2003.] Download references as BibTeΧ