Crash when Solve for Integral with 15C

09022017, 08:19 PM
Post: #41




RE: Crash when Solve for Integral with 15C
(09022017 01:24 PM)grsbanks Wrote:(09022017 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. It works fine for me  my program looks like this: 01 LBL "ECUBE" 02 MVAR "X" 03 RCL "X" 04 3 05 Y^X 06 E^X 07 END LLIM=0, ULIM=6; for ACC I tried 0 and 1E12, and the integration works fine with both (though it takes about 26 minutes with ACC=0). 

09022017, 08:24 PM
Post: #42




RE: Crash when Solve for Integral with 15C
(09022017 08:09 PM)Thomas Okken Wrote: 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 CLVed); in that case, INTEG behaves as with ACC=0. Thanks. Some quick checking reveals the 42S/Free42 create ACC (=0.0) if it doesn't exist when entering Integrate, but thereafter it is retained, like any other Real VAR, unless redefined or CLVed. Bob Prosperi 

09022017, 08:29 PM
(This post was last modified: 09022017 08:33 PM by Thomas Okken.)
Post: #43




RE: Crash when Solve for Integral with 15C
(09022017 08:24 PM)rprosperi Wrote:(09022017 08:09 PM)Thomas Okken Wrote: 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 CLVed); in that case, INTEG behaves as with ACC=0. Correct, but if you call INTEG without using the ∫f(x) menu, e.g. PGMINT "ECUBE" 0 STO "LLIM" 6 STO "ULIM" CLV "ACC" INTEG "X" ACC is not created. In other words, it is created by the ∫f(x) menu, not by the INTEG function. 

09022017, 08:34 PM
Post: #44




RE: Crash when Solve for Integral with 15C  
09022017, 08:48 PM
Post: #45




RE: Crash when Solve for Integral with 15C
(09022017 08:29 PM)Thomas Okken Wrote: Correct, but if you call INTEG without using the ∫f(x) menu, e.g. Those damn GUIs! Always doing stuff in the background, whether you ask them to or not. But in this case, it's a good thing. Bob Prosperi 

09022017, 08:55 PM
(This post was last modified: 09042017 10:38 AM by Gerson W. Barbosa.)
Post: #46




RE: Crash when Solve for Integral with 15C
(09022017 08:34 PM)Dieter Wrote:(09022017 08:14 PM)rprosperi Wrote: Ok, I just have to ask... why 216? Yes, because of the variable change suggested by you, BTW, as an attempt to improve the execution time. I did u=x^3 > x=u^(1/3) du/dx=3*x^2 > dx=du/(3*x^2) > Integ(e^x^3 dx, 0, 6) = 1/3*Integ(e^u/u^(2/3), 0, 216) Interestingly the speed improvement on the 34C, as reported by AndyGer, and the HP41CV (w/ Advantage ROM) is about only 20%, not so good as the 50% I had observed on the iOS HP15C emulator by HP. Gerson. PS: WA gives a closed form solution for the latter in terms of Gamma and Incomplete Gamma functions: 1/6(1+i*sqrt(3))*(Gamma(1/3)Gamma(1/3,6^3)) Unfortunately the Incomplete Gamma implementation on the WP34S won't handle these arguments. PPS: Edited to fix a typo per Bob Prosperi's observation below. PPPS: Edited again to add a 1/3 constant I had missed when transcribing my own handwritten note, as spotted by Pekis ahead. 

09022017, 09:06 PM
Post: #47




RE: Crash when Solve for Integral with 15C
(09022017 08:55 PM)Gerson W. Barbosa Wrote:(09022017 08:34 PM)Dieter Wrote: The integration limits have to be substituted, i.e. they are now 0³ = 0 and 6³ = 216. Thanks for breaking that down for us mere mortals Gerson. I had puzzled over it for a few moments and had just given up. Bob Prosperi 

09022017, 09:56 PM
Post: #48




RE: Crash when Solve for Integral with 15C
(09022017 09:06 PM)rprosperi Wrote: Thanks for breaking that down for us mere mortals Gerson. I had puzzled over it for a few moments and had just given up. You're much welcome, Bob! My fault as I didn't provide more information in the first place. It took me a while to remember how to do it by hand as well. Notice I'd replaced a 'u' for an 'e' in the second integral, which has been corrected now. Gerson. 

09022017, 10:11 PM
Post: #49




RE: Crash when Solve for Integral with 15C
(09022017 08:19 PM)Thomas Okken Wrote:(09022017 01:24 PM)grsbanks Wrote: 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. Thanks to you both. I can't think what I must have been doing wrong earlier. 

09022017, 11:29 PM
Post: #50




RE: Crash when Solve for Integral with 15C
(09022017 09:56 PM)Gerson W. Barbosa Wrote: You're much welcome, Bob! My fault as I didn't provide more information in the first place. It took me a while to remember how to do it by hand as well. Notice I'd replaced a 'u' for an 'e' in the second integral, which has been corrected now. That's quite alright. If you had explained it in the initial post, I likely would have just skimmed over it and spent no time thinking about (vs. the little time I did spend, but better little than none!) so by showing just the solution and a hint, it helped me to explore it and learn a bit more. But in the top line of the notes you show: u=x^3 > x=u^(2/3) Shouldn't x=u^(1/3) ? Bob Prosperi 

09032017, 12:57 AM
Post: #51




RE: Crash when Solve for Integral with 15C
(09022017 11:29 PM)rprosperi Wrote:(09022017 09:56 PM)Gerson W. Barbosa Wrote: You're much welcome, Bob! My fault as I didn't provide more information in the first place. It took me a while to remember how to do it by hand as well. Notice I'd replaced a 'u' for an 'e' in the second integral, which has been corrected now. Thank you for spotting yet a second typo. Fixed! Gerson. 

09032017, 02:36 AM
Post: #52




RE: Crash when Solve for Integral with 15C
(09032017 12:57 AM)Gerson W. Barbosa Wrote: Thank you for spotting yet a second typo. Fixed! Thank heavens for typos, else I would have been sooo confused. Thx! Bob Prosperi 

09032017, 06:36 AM
(This post was last modified: 09032017 07:45 AM by Gilles59.)
Post: #53




RE: Crash when Solve for Integral with 15C
I tried again with with the HP15LE,
SCI 4 HP15LE : 5.9639E91 in 7 seconds HP50G : 5.9639E91 in 17 seconds HP49G : 5.9639E91 ~ 40 seconds SCI 6 HP15LE : 5.963938E91 in 20 seconds HP50g : 5.963938E91 in 32 seconds HP49g : 5.963938E91 in ~ 65s All digits : 5.9639380919E91 in ~1mn with the 50G Always displaying "Running" with the 15LE after few minutes, I stopped by pressing ON 

09032017, 08:01 AM
(This post was last modified: 09032017 08:58 AM by brickviking.)
Post: #54




RE: Crash when Solve for Integral with 15C
For my two Casio fx9750s, I got the following results. fx9750g+ wouldn't integrate it, claiming a Ma Error on both the Gauss and Simpson methods. However, the fx9750GII SH4 (with the OS upgraded to 9760GII) gave me 5.963938092 E91 using this formula (where $ means integration symbol): $(f(x), lower, upper, tolerance). It took about 3.5 seconds for $(e^x^3, 0, 6, 0.001), about 5.8 seconds for 0.00001, about 10.6 seconds for 0.00000001 and about 12.3 seconds for 0.000000001.
My HP50G took about 1m5s $(0,6,e^x^3,x) >NUM and coughed up 5.9639380919 E91 with Std number format and 16 seconds with FIX4. Switching it back to Std coughed up 5.96393743779E91, but I expected this. What I didn't expect was that a Casio with SH4A (and no known FPU) clocked at 29.5MHz (or thereabouts), a supposedly inferior machine, came up with a significantly faster time than a calculator clocked roughly at 75MHz. EDIT: added data for clock speeds. (Post 72) Regards, BrickViking HP50g Casio fx9750G+ Casio fx9750GII (SH4a) 

09032017, 11:46 AM
Post: #55




RE: Crash when Solve for Integral with 15C
(09032017 08:01 AM)brickviking Wrote: What I didn't expect was that a Casio with SH4A (and no known FPU) clocked at 29.5MHz (or thereabouts), a supposedly inferior machine, came up with a significantly faster time than a calculator clocked roughly at 75MHz. The machine running at 75MHz is an ARM machine emulating a Saturn processor. The effective speed of the emulated Saturn machine is going to be far lower than 75MHz and quite possibly lower than your Casio's 29.5MHz. TTBOMK there is no FPU in the HP either. 

09032017, 06:47 PM
(This post was last modified: 09032017 06:54 PM by Gerson W. Barbosa.)
Post: #56




RE: Crash when Solve for Integral with 15C
375
« 0 DUP ROT FOR n n 3 * 1 + DUP n ! * 6 ROT ^ SWAP / + NEXT EXPAND →STR "/" " " SREPL DROP "'" " " SREPL DROP OBJ→ SWAP OVER IDIV2 ROT / →NUM →STR SWAP →STR SWAP + » EVAL => 5963938091897677519629167884945125687567068238536000 80366842664928717762274710443143932443681.0000000000 Only the first 22 digits are correct. 600+ terms would be necessary for 100 digits, but a clean 50g will run out of memory after around 380 terms. Also, it takes 414 seconds to get this result on the m48+ iOS emulator. Definitely neither the right tool nor the right method for this task, but it doesn't hurt trying. The series was obtained by integrating the Taylor series of the original integral, term by term. 

09032017, 07:38 PM
(This post was last modified: 09032017 07:40 PM by Matt Agajanian.)
Post: #57




RE: Crash when Solve for Integral with 15C
Gotta ask. Even using iPhone's version of Vicinno's 15E with FIX 6 accuracy, after 10 minites, still running. So I guess it's just the nature of e^(x^3) regardless of the calculator, laptop?


09032017, 08:00 PM
Post: #58




RE: Crash when Solve for Integral with 15C
(09032017 07:38 PM)Matt Agajanian Wrote: Gotta ask. Even using iPhone's version of Vicinno's 15E with FIX 6 accuracy, after 10 minites, still running. So I guess it's just the nature of e^(x^3) regardless of the calculator, laptop? Evaluating that integral to that degree of accuracy requires the integrand to be sampled 1023 times by the Romberg integrator in Free42. Depending on implementation details, other calculators may get there in one fewer iteration, which would mean 511 samples. This is all independent of the speed of the hardware on which you're running the calculation; I'm only talking about how often the function has to be executed. If you insert 1 STO+ 0 in your function somewhere, you can keep track of how often it is called, and at what rate. More than 1023 points to a buggy integrator; an invocation count that increases very slowly points to a slow calculator. 

09032017, 08:07 PM
Post: #59




RE: Crash when Solve for Integral with 15C
(09032017 08:00 PM)Thomas Okken Wrote:(09032017 07:38 PM)Matt Agajanian Wrote: Gotta ask. Even using iPhone's version of Vicinno's 15E with FIX 6 accuracy, after 10 minites, still running. So I guess it's just the nature of e^(x^3) regardless of the calculator, laptop? Counting iterationsClever! Thanks for the explanation and monitoring tactic. 

09042017, 12:42 AM
Post: #60




RE: Crash when Solve for Integral with 15C
(09032017 08:00 PM)Thomas Okken Wrote: If you insert 1 STO+ 0 in your function somewhere, you can keep track of how often it is called, and at what rate. More than 1023 points to a buggy integrator; an invocation count that increases very slowly points to a slow calculator. I was wondering how/where you were getting Fn evaluation counts. Clever! Simple! The best tips always are both. Thanks. Bob Prosperi 

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