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TI-36X Pro—Replace the batteries or just get a new one?
08-25-2019, 08:42 AM (This post was last modified: 08-25-2019 02:12 PM by jlind.)
Post: #72
RE: TI-36X Pro—Replace the batteries or just get a new one?
(01-20-2019 07:45 PM)pier4r Wrote:  
(01-19-2019 09:37 PM)ijabbott Wrote:  Test 6 - VBlogMag's \( e^{x^3} \) integration test

This is an integration test from VBlogMag's calculator benchmark video:
\[ \int_0^6 e^{x^3} dx \\
\text{Model} & \text{Time (s)} \\
\text{TI-30X Pro MP} & 8.6 \\
\text{TI-36X Pro} & 89.3 \\
\text{Casio fx-991EX} & 24.4
\end{array} \]

Nice work, thanks for sharing and great that you put the link to the sources!

Resurrecting this thread with a footnote after watching his video of this integral test . . .
The original integral interval was from -6 to +6, which he alludes to briefly at the beginning stating he had a problem with the HP-50g and changed the interval to half the original from 0 to +6. Had to replay the beginning of his video to spot the original interval on one of his calculator screens. I ran interval he had originally intended and it took over 17-1/2 minutes on the HP-50g versus the 1:05 he clocked for the modified interval from 0 to 6. As a test of this I ran the integral on a TI-Voyage 200 (about 3/4 the clock speed of a TI-89 Titanium) and clocked it at about 14 seconds using the 0 to +6 video interval and about 15.5 seconds with the -6 to +6 interval he originally intended to use. The anomaly among his fleet was the HP-50g and mine ran the 0 to +6 interval at almost exactly what his did. I suspect there's something in its (default ??) settings that consumes enormous clock cycles running in circles performing this integral test, especially over the original interval he had intended to use.

Nspire and Prime performance:
His video is 5 years old and these two had major updates last year (2018). The ARM processor in the latest Nspire CX II CAS released last year is cumulatively about 3x faster than than the CX CAS he used. Likewise the Prime G2 (model 2AP18AA, aka Rev D) is also about 3x faster than the Prime "G1" in the video. They were near instantaneous as-is. AFAIK, the Prime G2 is still only being distributed officially in Europe and hasn't been released to US distributors yet.

Thanks for sharing the timing tests. They have some interesting results, and if anyone runs them on multiple calculators, compare their numeric results as well. For me it's not just sheer speed. Decent precision is also important. A test run of these on some vintage HP and TI calculators would be interesting, which would take a bit of programming to set up.

TI-58 Benchmark:
Ran it on a TI-58 using Master Library Program 09, a Simpson approximation using intervals. Requires programming in the equation, invoking the library program, setting upper and lower bounds, and then the number of intervals. Tried 100 intervals but the precision was too far off. This integral has enormous area under it across that interval (f(-6) ~ 1.6 x10^-94, and f(6) ~ 6.4 x10^93). Ran it with 600 intervals for 0 to +6 which evaluates it with 0.01 spacing from 0 to +6. Took about 15 minutes (approximate). Still not happy with the ~2% precision of the answer (6.0nnnn x10^91). Churned away with it set to 1200 intervals, which took about a half hour and had 0.1% precision, about 1 part in 1,000 accuracy. With a TI-58's 4-bit uP you can make a pot of coffee with plenty of time to grind the beans beforehand, come back and have two cups while it's still churning away. Grumbling about the HP-50g but keeping in mind that all of the calculators he tested are orders of magnitude faster than the ones some of us used 40 years ago. :-)

SwissMicros DM42 Benchmark:
Set up similar program for f(x) and used the DM42's (Free42) definite integral function to calculate it from 0 to +6 with 1 x10^-11 set as the accuracy factor. Took about 14 seconds. Reset the lower bound to -6 and it took about 14.5 seconds. The definite integral routine in Free42 isn't a straightforward Simpson using a specified number of intervals. It keeps refining the intervals where needed to achieve the accuracy factor given. The DM42 has two clock speeds, one on internal battery power and substantially higher one when using external USB power. Plugged it in to a USB port and ran it again. Times dropped to ~5.5 seconds for 0 to +6 and just under 6 seconds for -6 to +6, more than twice as fast. From -6 to -1 for this function, there is near zero area under the curve compared to the monstrous area from about ~1 to 6. Plot f(x) and you'll see how devilish this function is from -6 to +6 which puts f(x) very near some calculator limits in smallest and largest values. ;-)

Regarding the OP's original question . . .
I trust he has either replaced the battery or the calculator by now (I'd have gutted it and replaced the battery, posting photos of its open heart surgery on Fakebook). Regarding precision and speed, there's plenty of data on the Internet for (nearly) all the major calculators' makes and models going back to the early 1970's. The discussion about the TI-30X Plus MathPrint has piqued my interest. I need another scientific pocket calculator like another hole in my head. If it were about 3/4" shorter I'd be more likely to buy one.



Pickett: N4-ES, N600
TI: 58, 30-III, 30x Pro MathPrint, 36x Solar, 85, 86, 89T, Voyage 200, Nspire CX II CAS
HP: 50g, Prime G2, DM42
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RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-25-2019 08:42 AM

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