Would a question asking an unimplemented feature about a fully working script be on-topic here?

Two days ago (or yesterday depending on your timezone) was π-day. So I thought it was a good day to calculate π.

I used Machin-like formula to calculate π, in homage of William Shanks, who calculated 527 correct digits of π well before electronic computers. Though I used Newton's Accelerated Arctangent Series and I got my terms from here.

I rewrote the arctangent series to make it do everything in integer domain.

And it works. See this Stack Overflow question for an earlier iteration of my implementation.

Now I have re-implemented it again so that I can get as many correct digits of π as I want without using any libraries, and using these terms: ((44, 57), (7, 239), (-12, 682), (24, 12943)), I was able to get the first 1024 decimal places of π in 292 iterations:

In [139]: Machin_Pi.get_n_places(4, 1024)
Out[139]:
(292,
 '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788')

But I haven't been able to accelerate the convergence of the series further, I have tried to make it converge faster by using binary split (though if I understand correctly it gets the same result in less iterations?), but I cannot make it work, my math is very rusty, I am a high-school dropout and the last year I attended school was 2017...

Would such a question be on topic if I am asking to make the series converge faster?