Machin-like formulae
M000000426
$$\pi=28\arctan\left(\frac{1}{10}\right)+8\arctan\left(\frac{1}{50}\right)+16\arctan\left(\frac{1}{100}\right)+4\arctan\left(\frac{1}{682}\right)+16\arctan\left(\frac{1}{1000}\right)+12\arctan\left(\frac{1}{1303}\right)-16\arctan\left(\frac{1}{90109}\right)$$
Compact formula
28[10] + 8[50] + 16[100] + 4[682] + 16[1000] + 12[1303] - 16[90109]
Lehmer's measure
3.29766
References
Wrench Jr., J. W. The derivation of arctangent equalities (PhD thesis, Yale University), 1938.
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