M000196

$$\pi=57905980\arctan\left(\frac{1}{82189674}\right)+216229020\arctan\left(\frac{1}{159358932}\right)-16449028\arctan\left(\frac{1}{162166243}\right)+260303248\arctan\left(\frac{1}{213495433}\right)+141105228\arctan\left(\frac{1}{225823278}\right)-100283292\arctan\left(\frac{1}{284862638}\right)-88924240\arctan\left(\frac{1}{403478642}\right)-23319688\arctan\left(\frac{1}{657922943}\right)+30022892\arctan\left(\frac{1}{727507932}\right)-94775960\arctan\left(\frac{2}{1498434239}\right)+100294784\arctan\left(\frac{2}{4417955351}\right)-95685024\arctan\left(\frac{1}{7804016832}\right)-50397484\arctan\left(\frac{2}{27894683333}\right)+58423876\arctan\left(\frac{2}{74522099649}\right)-135191184\arctan\left(\frac{1}{293153860797}\right)-100794968\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula57905980[82189674] + 216229020[159358932] - 16449028[162166243] + 260303248[213495433] + 141105228[225823278] - 100283292[284862638] - 88924240[403478642] - 23319688[657922943] + 30022892[727507932] - 94775960[1498434239/2] + 100294784[4417955351/2] - 95685024[7804016832] - 50397484[27894683333/2] + 58423876[74522099649/2] - 135191184[293153860797] - 100794968[169838669284032]
Lehmer's measure1.74199
References
MRW (12Aug06)(ΒΆΒΆ1.88563) (full reference coming soon)