The Hwang equation is not the most efficient Machin like formula to compute $\pi$. The following formula

$${\pi \over 4} = 32 \, \hbox{arctan}({1\over 40}) - \hbox{arctan}\biggl(
{38035138859000075702655846657186322249216830232319
\over
2634699316100146880926635665506082395762836079845121}\biggr)
$$
has a Lehmer's measure around $1.16751$ thus beating Hwang's formula (with Lehmer's measure $1.51240$). 

Abrarov and Quine gave a formula with Lehmer's measure $0.245319$ last summer, together with the relevant algorithms, in their paper [An iteration procedure for a two-term Machin-like formula for pi with small Lehmer’s measure](https://arxiv.org/abs/1706.08835). That formula provides 16 new digits of $\pi$ per term increment thus beating the famous Chudnovsky formula.

At $k=27$ the Abrarov-Quine formula gives a fraction that has a numerator with $522\,185\,807$ digits and a denominator with $522\,185\,816$ digits. This type of fractions with huge numbers can also be obtained from the Borwein’s integral as shown in the preprint by Uwe Bäsel and Robert Baillie [Sinc integrals and tiny numbers](https://arxiv.org/pdf/1510.03200) such that a formula for $\pi$ can be written with $453\,130\,145$ and $453\,237\,170$ digits in numerator and denominator, respectively.