001- 1 016- +

002- 0 017- 1/x

003- x<>y 018- STO 1

004- y^x 019- RCL 0

005- STO 0 020- 3

006- ENTER 021- CHS

007- * 022- y^x

008- g LSTx 023- STO+ 1

009- 2 024- 1

010- * 025- STO- 0

011- 1 026- RCL 0

012- + 027- g x=0

013- x<>y 028- g GTO 30

014- 2 029- g GTO 19

015- * 030- RCL 1

031- g GTO 00

Given the proper argument this small HP-12C program will give a meaningful result in about 2 minutes on the classic HP-12C (under a couple of seconds on the HP-12C+).

Very nice!

Not having a 12C to hand, I converted this for the 34S:

01: LBL A

02: 10[^x]

03: STO 00

04: x[^2]

05: RCL L

06: RCL+ X

07: INC X

08: x[<->] Y

09: RCL+ X

10: +

11: 1/x

12: STO 01

13: LBL 00

14: RCL 00

15: 3

16: +/-

17: y[^x]

18: STO+ 01

19: DSZ 00

20: GTO 00

21: RCL 01

22: RTN

However, there is an alternative WP 34S program that produces the same limit using *four* steps *including* the LBL at the start and the RTN at the end -- so *two* steps of working code.

- Pauli

Drat, missed some optimisation in the above code. Change line 18 to + and delete lines 21 and 12.

- Pauli

Quote:

However, there is an alternative WP 34S program that produces the same limit using four steps including the LBL at the start and the RTN at the end -- so two steps of working code.

Actually, I've tested my results upon the WP 34S function :-)

Gerson.

I thought of including "optimization of the code is left as an exercise to the reader", but then I realized figuring out what the program did was good exercise enough. That was my first attempt after I noticed it this afternoon. Without the trick, about 50k terms would have to be computed in order to get the same result.

Gerson.

While we're at it, here's another one for another constant:

001- 1 019- CHS

002- 0 020- STO+ 0

003- x<>y 021- STO* 2

004- y^x 022- RCL 0

005- STO 0 023- 2

006- ENTER 024- *

007- * 025- +

008- 8 026- ENTER

009- * 027- *

010- 6 028- 1/x

011- + 029- RCL 2

012- 1/x 030- *

013- STO 1 031- STO+ 1

014- 1 032- RCL 0

015- STO+ 0 033- g x=0

016- STO+ 1 034- g GTO 36

017- STO 2 035- g GTO 18

018- 1 036- RCL 1

037- g GTO 00

Checking the archives, I found an old mini-challenge of Valentin's which is worth mentioning. Crawl's program in Message #52 appears to explore the same idea. I certainly read the thread at the time, but I'd completely forgotten about his particular program. It's worth reading Valentin's original solutions and other therein:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv016.cgi?read=95861

I've come up with a slightly faster series. I've started to implement it on the HP-15C LE, but the initialization alone takes up 37 steps. If I manage to optimize it a bit, I'll present it later.