Crash when Solve for Integral with 15C

[Gamo]

With this integral problem it crash when used the 15C app for Android but 15C Virtual Calculator for Windows PC is running fine and took about almost 1 minute to solve.
I don't have physical HP 15C to try just like to know if it crash that too.

To solve:
Set the program
g P/R
f PRGM
LBL 0
3
y^x
e^x
g RTN
g P/R

To run integral
0 ENTER 6 [f] [∫xy] [0]

Answer: 5.9639 91

Link to the clip: https://youtu.be/QiTh7n3wRRE


Here is the problem attached as jpg.

Gamo

[rprosperi]

(08-31-2017 01:21 PM)Gamo Wrote:  With this integral problem it crash when used the 15C app for Android but 15C Virtual Calculator for Windows PC is running fine and took about almost 1 minute to solve.
I don't have physical HP 15C to try just like to know if it crash that too.

Here is the problem attached as jpg.

Gamo

For reproducing/testing a bug, please provide the exact program/entry steps you used. It can be done more than 1 way, and the problem may be related to how you entered it.

[SlideRule]

Gamo

The integral is discussed quite well at How to Evaluate e^x^3

BEST!
SlideRule

ps: it crashes a Casio as well

[Gilles59]

After à long time i get "pr error" with the HP15c-le (but im a poor user with the 15c perhaps i do something wrong)

Works fine on the 50g

[BobVA]

(08-31-2017 06:34 PM)Gilles59 Wrote:  After à long time i get "pr error" with the HP15c-le

That's a "power error", so perhaps the batteries are getting a bit low and the long run time dragged them down far enough to cause a reset?

[Not a direct answer to the OP's question, but my LE was also taking *quite* awhile to run this, so I replaced the initial exponentiation with two multiplications. It still took about five minutes to produce the same result noted in the original post. Maybe you can try this in the app? That might at least narrow down where the problem is occurring?]

Bob

[SlideRule]

Gamo

From the aforementioned url:
"It is very common for an elementary function not to have an elementary antiderivative. Proving this is the case for a particular function can be difficult. Your function e^x^3 happens to be one for which the standard method for showing "impossibility," which dates back in principle to Liouville, works reasonably smoothly. Many non-elementary "special functions" have been devised such that useful integrals can be expressed in terms of these special functions. I would guess that Maple, or Mathematica, even Wolfram Alpha, can produce an answer in terms of some special function."
from Wolfram Alpha
[attachment=5146]
"The antiderivative of e^x^3 cannot be expressed in terms of elementary functions. We can, however, express it using power series... another try you can solve it with Gamma function... finally ... The integral cannot be evaluated. We have to use power series of exponent and then integral term by term., or use a substitution.

BEST!
SlideRule

[rprosperi]

Gamo,

Thanks for the program steps.

Which 15C Virtual Calculator are you using on Windows?

I've tested it on Torsten Manz' 15C simulator running on Win-7 and on a SwissMicros DM15L. Both are still "running" after well more than 5 minutes. No crash or error messages, they're just running and running. I got tired of waiting so added this reply. I'll update with results if anything ever appears.

Update: They just kept on running... with no anwer.

While waiting , I also tried it in the DM42 and it got the same answer in 2-3 seconds.

[Gamo]

Hello rprosperi

I'm using the original HP 15C Virtual Calculator from HP for Windows PC this is the only one that run through without any problem in about 1 minute.

I did try this on HP Prime App for Android and it crash when execute in Home mode. On CAS mode the error message appear and gave the answer instantly.

HP Prime Virtual Calculator for Windows PC also crash and the application close altogether.

Gamo

[SlideRule]

Gamo

Perhaps this attached GRAPH will help?
[attachment=5148]
or the following url Functions without Antiderivatives by TR Smith with the follwing extract:
"Exponential Functions
Here is a list of basic exponential forms that have no antiderivatives
• e^(x^2) and e^(-x^2)
• e^(x^3) and e^(-x^3)
• More generally, e^(x^n) and e^(-x^n) are non-integrable for all integers n greater than 1.
• e^(1/x) and e^(-1/x) (See link for approximate integration technique.)
• e^(1/x^2) and e^(-1/x^2)
• More generally, e^(1/x^n) and e^(-1/x^n) are non integrable for all positive integers n."

BEST!
SlideRule

[Gerson W. Barbosa]

(08-31-2017 05:44 PM)SlideRule Wrote:  ps: it crashes a Casio as well

Not the fx-991 CLASSWIZ: 5.963938092x10^91 in 25 seconds.

[Dieter]

(09-01-2017 01:40 AM)SlideRule Wrote:  Perhaps this attached GRAPH will help?
(...)
or the following url Functions without Antiderivatives by TR Smith with the follwing extract:
[i][color=#FF0000]"Exponential Functions
Here is a list of basic exponential forms that have no antiderivatives
• e^(x^2) and e^(-x^2)
• e^(x^3) and e^(-x^3)
(...)

Yes, the function has no closed form antiderivative. But that does not matter here because the 15C is calculating a definite integral by numeric integration. Exactly because there is no analytic solution. ;-)

For the math geeks: somehow I feel that in this case some variable substitution should be applied to calculate the integral easier and faster. Maybe someone has an idea here?

Dieter

[SlideRule]

(09-01-2017 05:47 AM)Dieter Wrote:  For the math geeks: somehow I feel that in this case some variable substitution should be applied to calculate the integral easier and faster. Maybe someone has an idea here?
Dieter

Perhaps post#3, #6 or #9?

BEST!
SlideRule

ps: there is an excellent paper Nonelementary Antiderivatives by Dana P. Williams (Dartmouth college) with specific reference to e^x^2: a good read & very edifying!

[emece67]

\(5.963938091897677519629320420205\underline{665}×10^{91}\) in a wp34s after 2'20''.
\(5.9639×10^{91}\) in a DM15L after 50'.

[rprosperi]

(09-01-2017 11:51 AM)emece67 Wrote:  \(5.9639×10^{91}\) in a DM15L after 50'.

Ah, I see. I guess I'm not patient enough; If only I waited 20 more minutes, I could have posted this first, lol.

[Gerson W. Barbosa]

(09-01-2017 01:24 PM)rprosperi Wrote:  

(09-01-2017 11:51 AM)emece67 Wrote:  \(5.9639×10^{91}\) in a DM15L after 50'.

Ah, I see. I guess I'm not patient enough; If only I waited 20 more minutes, I could have posted this first, lol.

Less than 2 and a half minutes here:

5.963938096E91 (FIX 9)

HP-15C Emulator for iOS by HP

LBL 0
x^2
*
e^x
RTN

Not patient enough to try it on the HP-15C LE, though.

Gerson.

[emece67]

(09-01-2017 01:24 PM)rprosperi Wrote:  

(09-01-2017 11:51 AM)emece67 Wrote:  \(5.9639×10^{91}\) in a DM15L after 50'.

Ah, I see. I guess I'm not patient enough; If only I waited 20 more minutes, I could have posted this first, lol.

Sorry, it should be:
\(5.9639×10^{91}\) in a DM15L after 50''.

My DM15L was running at 48 MHz. If switched to 12 MHz it takes around 3 minutes.

[rprosperi]

(09-01-2017 05:36 PM)emece67 Wrote:  Sorry, it should be:
\(5.9639×10^{91}\) in a DM15L after 50''.

My DM15L was running at 48 MHz. If switched to 12 MHz it takes around 3 minutes.

I just tried again, and again my DM15L ran for 10 minutes with no result.

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.

Though it is specifically discussed, the manual is not completely clear (to me) about how display mode affects results, but it seems to have a dramatic impact. I would expect a setting with 2 digits of accuracy (FIX 2) would have finished faster than with 4 (SCI 4) since even when set to FIX mode, it switches to SCI mode as needed if the magnitude under/overflows.

Perhaps some of the other error and/or endless calculating errors reported above were also affected by the same issue. Try again using SCI 4 mode.

Thanks for the correction emece67; it motivated me to explore this further and learn a bit in the process.

[Dieter]

(09-02-2017 02:41 AM)rprosperi Wrote:  Though it is specifically discussed, the manual is not completely clear (to me) about how display mode affects results, but it seems to have a dramatic impact.

Yes. Maybe you should take a look at the respective section in the 15C Advanced Functions Handbook.

(09-02-2017 02:41 AM)rprosperi Wrote:  I would expect a setting with 2 digits of accuracy (FIX 2) would have finished faster than with 4 (SCI 4) since even when set to FIX mode, it switches to SCI mode as needed if the magnitude under/overflows.

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.

(09-02-2017 02:41 AM)rprosperi Wrote:  Perhaps some of the other error and/or endless calculating errors reported above were also affected by the same issue. Try again using SCI 4 mode.

Yes, for a first result I'd say even SCI 2 is fine. If you need more simply repeat the calculation with SCI 4, SCI 6 etc.

Dieter

[Gerson W. Barbosa]

(09-01-2017 05:47 AM)Dieter Wrote:  somehow I feel that in this case some variable substitution should be applied to calculate the integral easier and faster. Maybe someone has an idea here?

By making u=x^3 the integral can be evaluated twice as fast on the HP-15C emulator:

2 ENTER 3 / STO 0

LBL 0
e^x
LASTx
RCL 0
y^x
/
RTN

0 ENTER 216 Intxy 3 / => 5.963938097E91 (1'15")

Gerson.

[Vincent Weber]

Various tests in SCI 4 mode of the original program posted:

-HP app on Android: straight crash of the app. Well done, HP, with your own material. We know that the HP way is dead...

-HP app on iOS, latest beta (I am part of the beta program): surprisingly better, returns the correct answer in a few seconds... But strangely, the LCD is blinking, as if an error has occured..

-Olivier de Smet's go15c on Android at max speed: correct answer in 2 seconds, no blinking.

None of these behave well in FIX 9 mode. The HP Android app still crashes immediately. The other too seem to run forever even go15c in max mode.

Trying now on a real 15C (the original, not the buggy LE) will revert.

Cheers