Machin-like formulae
M000315
$$\pi=256\arctan\left(\frac{1}{80}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-32\arctan\left(\frac{1}{4030}\right)-64\arctan\left(\frac{1}{32060}\right)-128\arctan\left(\frac{1}{256120}\right)$$
Compact formula
256[80] - 4[239] - 16[515] - 32[4030] - 64[32060] - 128[256120]
Lehmer's measure
1.99886
References
CASHMORE
(full reference coming soon)