Crash when Solve for Integral with 15C

[Vincent Weber]

I think I exhausted the real calc batteries with this thing - the calc shut off displaying "*" blinking.

I also launched it a x1 speed on go15c. Successful completion in 35 minutes.

Congrats Olivier !

[hibiki]

I left my physical HP-15C, HP-34C and HP32SII calculating for more than 1 hour and finally I gave up and halted the processing (but no crash happened). In my HP-35S it was calculated in less than 1 minute.

[grsbanks]

(09-02-2017 02:41 AM)rprosperi Wrote:  Then it occurred to me that I was running in FIX 2 mode, which could be affecting behavior. So I changed display mode to SCI 4, and I then got the same result in about the same time as your results.

Bingo! The display format is why my DM15L just kept on running. Should have remembered that is how it derives (no pun intended) its accuracy.

What accuracy and display format did you use when you tested this on the DM42? I just get an "Out of range" error when attempting the integration.

[rprosperi]

(09-02-2017 05:53 AM)Dieter Wrote:  The result is about 6 E+91. FIX 2 means two digits after the decimal point, so that's actually 94 significant digits, in other words: it's (more than) full machine precision you're demanding. On the other hand SCI 4 sets only five significant digits which is returned much faster.

Thanks Dieter. All this makes sense to me, as is so often the case, after the explanation. Though I initially would have guessed that the 15C would treat FIX 2 as 2 significant places, even if it must shift to SCI mode, just as it does when the displayed number must be so shifted. Though subtle, this is a significant difference and highlights how the machine handles the numbers internally (vs. display) and so is an interesting exercise. I will read the referenced section in the 15C AF HB. Again! AFAIK, this is the best treatment of such topics in any HP manual; can you recommend others I may have missed?

[rprosperi]

(09-02-2017 01:24 PM)grsbanks Wrote:  What accuracy and display format did you use when you tested this on the DM42? I just get an "Out of range" error when attempting the integration.

I tested on the DM42 before I woke up and considered the display mode impact, so I'm not 100% sure. I'd guess it was in (my) default of FIX 2, but need to check. I'll update this when I can later today.

Update: Looking at the DM42 reminded me (still in last used status) of the sequence of events. My DM42 was in SCI 04 mode when I first ran it there. It had been in this mode from some prior dabbling, and after it succeeded almost instantly, it was seeing the result in this mode that prompted me to consider changing display mode on the DM15L, leading to success there.

I just ran it again, and it definitely produces 5.9639E91 within 2 seconds.

[Joe Horn]

Speeding up integrals by controlling integration accuracy by adjusting the display setting goes back to the very beginning:

"Numerical integration was also new to the HP-34C. ... The user could adjust the time spent integrating by telling the calculator how many digits were significant. This controlled the integration step size and was done by simply setting the display format to show no more digits than required in the final answer. The Manual devoted a 32 page appendix to a more detailed description of the integration function."

-- excerpt from the HP-34C page at the famous, fabulous Museum of HP Calculators.

[Thomas Okken]

(09-02-2017 01:45 PM)rprosperi Wrote:  

(09-02-2017 01:24 PM)grsbanks Wrote:  What accuracy and display format did you use when you tested this on the DM42? I just get an "Out of range" error when attempting the integration.

I tested on the DM42 before I woke up and considered the display mode impact, so I'm not 100% sure. I'd guess it was in (my) default of FIX 2, but need to check. I'll update this when I can later today.

Update: Looking at the DM42 reminded me (still in last used status) of the sequence of events. My DM42 was in SCI 04 mode when I first ran it there. It had been in this mode from some prior dabbling, and after it succeeded almost instantly, it was seeing the result in this mode that prompted me to consider changing display mode on the DM15L, leading to success there.

I just ran it again, and it definitely produces 5.9639E91 within 2 seconds.

On the DM42 (and Free42 and HP-42S), accuracy of integration is not controlled by the display mode, but by the ACC variable. ACC is a relative error, so ACC = 0.001 gives three digits. Leaving ACC unset, or set to something <= 0 gives maximum precision, which can take a long time.

[AndiGer]

(09-02-2017 11:31 AM)hibiki Wrote:  I left my physical HP-15C, HP-34C and HP32SII calculating for more than 1 hour and finally I gave up and halted the processing (but no crash happened). In my HP-35S it was calculated in less than 1 minute.

Set my physical HP-34C to SCI-4. Ended up with the expected result after exactly 21'. IMHO ok for one of the first or even first (don't know) handheld offering numerical integration.
Andi

[AndiGer]

(09-01-2017 02:14 PM)Gerson W. Barbosa Wrote:  LBL 0
x^2
*
e^x
RTN

Gerson

Added a LSTx between x^2 and *. Worked it thru in about 14' on the HP-34C.
Andi

[Dieter]

(09-02-2017 05:19 PM)AndiGer Wrote:  

(09-01-2017 02:14 PM)Gerson W. Barbosa Wrote:  LBL 0
x^2
*
e^x
RTN

Gerson

Added a LSTx between x^2 and *.

A LastX should not be required as the stack is filled with x, i.e. both X, Y, Z and T contain the current x-value. This is true for the Solve and Integrate functions of the 34C, 15C, the WP34s and probably other HPs as well.

(09-02-2017 05:19 PM)AndiGer Wrote:  Worked it thru in about 14' on the HP-34C.

For which display setting?

Dieter

[Dieter]

(09-02-2017 01:40 PM)rprosperi Wrote:  Thanks Dieter. All this makes sense to me, as is so often the case, after the explanation. Though I initially would have guessed that the 15C would treat FIX 2 as 2 significant places,

Well, a tolerance of ±0,01 (FIX 2) means a relative error of 1E–6 for x=10000 while it's 1% for x=1. Or even 100% for x=0,01. This makes quite a difference. ;-)

(09-02-2017 01:40 PM)rprosperi Wrote:  Though subtle, this is a significant difference and highlights how the machine handles the numbers internally (vs. display) and so is an interesting exercise.

Actually the display format specifies the accuracy of the integrand, not the integral. That's another subtle difference, and you might want to read more about this in the 15C Advanced functions handbook and/or one of the other sources below.

(09-02-2017 01:40 PM)rprosperi Wrote:  I will read the referenced section in the 15C AF HB. Again! AFAIK, this is the best treatment of such topics in any HP manual; can you recommend others I may have missed?

Sure: first there is the original HP34C manual that discusses integration in detail. This refers to the original implementation which AFAIK was also used for the 15C. Then there is an article by W. Kahan in the August 1980 HP Journal issue where the new functions of the 34C (Solve and Integrate) are introduced and discussed.

Dieter

[Thomas Okken]

(09-02-2017 05:35 PM)Dieter Wrote:  

(09-02-2017 05:19 PM)AndiGer Wrote:  Added a LSTx between x^2 and *.

A LastX should not be required as the stack is filled with x, i.e. both X, Y, Z and T contain the current x-value. This is true for the Solve and Integrate functions of the 34C, 15C, the WP34s and probably other HPs as well.

Not for the HP-42S; it doesn't put anything on the stack when it calls the function, but instead passes the parameters through named variables.

Speaking of the HP-42S, it gets 12 correct digits in 7'12" with ACC=0, evaluating the function 2047 times.

[Gerson W. Barbosa]

(09-02-2017 05:19 PM)AndiGer Wrote:  

(09-01-2017 02:14 PM)Gerson W. Barbosa Wrote:  LBL 0
x^2
*
e^x
RTN

Gerson

Added a LSTx between x^2 and *. Worked it thru in about 14' on the HP-34C.
Andi

6'35" on my 41CV w/ Advantage ROM. SCI 4, result = 5.9639E91. No extra instruction needed as Dieter has explained above.

Gerson.

[Gerson W. Barbosa]

(09-02-2017 06:25 PM)Gerson W. Barbosa Wrote:  6'35" on my 41CV w/ Advantage ROM. SCI 4, result = 5.9639E91.

Or, equivalently:

2 ENTER 3 / STO 0

LBL 'EE
E^X
LASTX
RCL 0
Y^X
/
RTN

0 ENTER 216 ALPHA EE ALPHA XEQ ALPHA INTEG ALPHA => 1.7892E92 (5'17")

3 / => 5.9639E91

[klesl]

casio fx-991CE X approx. 23 seconds - 5,963938092×10^91
casio fx-9700GE approx. 23 seconds - 6×10^91
casio fx-cg50 almost immediately (maybe 2 seconds) - 5,963938092×10^91
casio fx-5800P approx. 40 seconds - 5,963938092×10^91
casio fx-3650P II approx. 115 seconds - 5,963938092×10^91
sharp el-9950 almost immediately (maybe 2 seconds) - 5,963938092×10^91
sharp el-w506x approx. 14 seconds - 7,466216848×10^91 (n=100, default value),
144 seconds - 5,964300819×10^91 (n=1000)
sharp el-506x approx. 123 seconds - 5,964300819×10^91 (n=1000)
canon F-792SGA approx. 80 seconds - 5,963938092×10^91
canon X Mark I Pro approx. 79 seconds - 5,963938092×10^91
ti-30x pro approx. 82 seconds - 5,963938091×10^91

[AndiGer]

(09-02-2017 05:35 PM)Dieter Wrote:  A LastX should not be required as the stack is filled with x, i.e. both X, Y, Z and T contain the current x-value. This is true for the Solve and Integrate functions of the 34C, 15C, the WP34s and probably other HPs as well.

I forgot / was no more aware of these days.

(09-02-2017 05:35 PM)Dieter Wrote:  For which display setting?

Same as before: SCI4

Removed LSTx. Time required: about 13'20''

[AndiGer]

(09-02-2017 06:42 PM)Gerson W. Barbosa Wrote:  

(09-02-2017 06:25 PM)Gerson W. Barbosa Wrote:  6'35" on my 41CV w/ Advantage ROM. SCI 4, result = 5.9639E91.

Or, equivalently:

2 ENTER 3 / STO 0

LBL 'EE
E^X
LASTX
RCL 0
Y^X
/
RTN

0 ENTER 216 ALPHA EE ALPHA XEQ ALPHA INTEG ALPHA => 1.7892E92 (5'17")

3 / => 5.9639E91

Integral transformation as Gerson suggests: SCI4 is 11' on my HP34C

[rprosperi]

(09-02-2017 03:11 PM)Thomas Okken Wrote:  On the DM42 (and Free42 and HP-42S), accuracy of integration is not controlled by the display mode, but by the ACC variable. ACC is a relative error, so ACC = 0.001 gives three digits. Leaving ACC unset, or set to something <= 0 gives maximum precision, which can take a long time.

I used ACC=.001 for my test runs.

I always set ACC out of habit, but I assume your note means that ACC is reset (or unset) each time you enter the Integral function (as opposed to re-using the value last used)?

[Thomas Okken]

(09-02-2017 07:57 PM)rprosperi Wrote:  

(09-02-2017 03:11 PM)Thomas Okken Wrote:  On the DM42 (and Free42 and HP-42S), accuracy of integration is not controlled by the display mode, but by the ACC variable. ACC is a relative error, so ACC = 0.001 gives three digits. Leaving ACC unset, or set to something <= 0 gives maximum precision, which can take a long time.

I used ACC=.001 for my test runs.

I always set ACC out of habit, but I assume your note means that ACC is reset (or unset) each time you enter the Integral function (as opposed to re-using the value last used)?

No, INTEG doesn't change or unset ACC. I was referring to the case in which the ACC variable doesn't exist (hasn't been created, or has been CLV-ed); in that case, INTEG behaves as with ACC=0.

[rprosperi]

(09-02-2017 06:42 PM)Gerson W. Barbosa Wrote:  Or, equivalently:

2 ENTER 3 / STO 0

LBL 'EE
E^X
LASTX
RCL 0
Y^X
/
RTN

0 ENTER 216 ALPHA EE ALPHA XEQ ALPHA INTEG ALPHA => 1.7892E92 (5'17")

3 / => 5.9639E91

Ok, I just have to ask... why 216?