M000000213: Takano's formula

$$\pi=48\arctan\left(\frac{1}{49}\right)+128\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+48\arctan\left(\frac{1}{110443}\right)$$

Name	Takano's formula
Compact formula	`48[49] + 128[57] - 20[239] + 48[110443]`
Lehmer's measure	1.77990
Notes	In 2022, this formula was used alongside M000059 to compute 1,241,100,000,000 decimal places of π.
References	Takano, Kikuo. Pi no arctangent relation wo Motomete, BIT 15(4), 83–91, 1983. Download references as BibTeΧ