Machin-like formulae

M000482

$$\pi=283704\arctan\left(\frac{1}{157552}\right)+337164\arctan\left(\frac{1}{330182}\right)-25016\arctan\left(\frac{1}{485298}\right)+211480\arctan\left(\frac{1}{619858}\right)+119444\arctan\left(\frac{1}{780262}\right)-190076\arctan\left(\frac{1}{1460857}\right)-111056\arctan\left(\frac{1}{4218932}\right)+46360\arctan\left(\frac{1}{5982670}\right)+193768\arctan\left(\frac{1}{9548768}\right)+199704\arctan\left(\frac{1}{33853568}\right)-108224\arctan\left(\frac{1}{231373438}\right)$$
Compact formula283704[157552] + 337164[330182] - 25016[485298] + 211480[619858] + 119444[780262] - 190076[1460857] - 111056[4218932] + 46360[5982670] + 193768[9548768] + 199704[33853568] - 108224[231373438]
Lehmer's measure1.74817
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

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