Pi Approximation Day

[C.Ret]

(07-23-2022 03:41 PM)Gerson W. Barbosa Wrote:  

(07-23-2022 03:18 PM)C.Ret Wrote:  Is this a specific HP-42S trick, does memory recall arithmetic modify the LAST register?

Yes, it does, unlike memory store arithmetic:

Thank you for your quick response; this is a different behavior from the HP-15C memory recall arithmetic logic. That explain why I was so lost.

001 LBL "WLP
002 10
003 ENTER^
004 LBL 00
005 RCL Y
006 X^2
007 LASTX
008 +
009 -3
010 Y^X
011 -
012 DSE Y
013 GTO 00
014 SQRT
015 END

With FIX 7 display format, this little program give a better approximation of PI than 22/07.
Surprisingly, the number of instructions is the same as Valentin Albillo's original code.

\( \sqrt{10-\frac{1}{\left ( 10^2+10 \right )^3}-\frac{1}{\left ( 9^2+9 \right )^3}-\frac{1}{\left ( 8^2+8 \right )^3}-\cdots -\frac{1}{\left ( 2^2+2 \right )^3}-\frac{1}{\left ( 1^2+1 \right )^3}} = \sqrt{ \frac{2\,780\,722\,699}{281\,746\,080} } \approx \pi \)