Machin-like formulae
M000000520
$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{7}\right)+16\arctan\left(\frac{1}{21}\right)-8\arctan\left(\frac{1}{38}\right)$$
Compact formula
16[5] - 4[7] + 16[21] - 8[38]
Lehmer's measure
4.00327