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. That formula provides 16 new digits of $\pi$ per term increment thus beating the famous Chudnovsky formula.
The Abrarov-Quine formula won't fit on that small answer box though since one of the fraction has a numerator with $522\,185\,807$ digits and a denominator with $522\,185\,816$ digits.