TI-36X Pro—Replace the batteries or just get a new one?

[ijabbott]

There is a difference in the 'Calculator Forensics Test' result for the following trigonometric calculation in degrees mode: sin⁻¹(cos⁻¹(tan⁻¹(tan(cos(sin(9)))))).

• The old TI-36X Pro (and TI-30X Pro MultiView) produces the result 9.000001077 to ten figures (internal result 9.000001077372).
• The new TI-30X Pro MathPrint produces the result 8.999999860 to ten figures (internal result 8.999999860032).
  

The result from the new model is closer to the actual value of 9.

[klesl]

(01-13-2019 05:01 AM)lrdheat Wrote:  Those new functions make it possible to choose an epsilon in MathPrint. On the 36X Pro, the epsilon could only be user chosen in the classic mode.

I don't see those new functions in classic mode on TI-30X Pro Multiview - still 6 functions in menu "math - math" and no list ops after pressing menu data twice.

[ijabbott]

(01-13-2019 08:27 PM)klesl Wrote:  

(01-13-2019 05:01 AM)lrdheat Wrote:  Those new functions make it possible to choose an epsilon in MathPrint. On the 36X Pro, the epsilon could only be user chosen in the classic mode.

I don't see those new functions in classic mode on TI-30X Pro Multiview - still 6 functions in menu "math - math" and no list ops after pressing menu data twice.

The nDeriv and fnInt functions aren't present in the math menu on TI-30X Pro MultiView (or TI-36X Pro), but if the calculator is set to classic mode, you can enter 'nDeriv(' via '2nd' 'd/dx□', or enter 'fnInt(' via '2nd' '∫:□dx'. Then you can enter the epsilon value as an optional final parameter of the function.

You are correct that there are no list ops after pressing menu data twice on the older calculators. It's a new feature on the TI-30X Pro MathPrint.

[Albert Chan]

(01-13-2019 07:28 PM)ijabbott Wrote:  In the new TI-30X Pro MathPrint, unit conversions seem to have a much lower priority, so that '-1 °C⯈°F' and '2-3 °C⯈°F' both produce a result of 30.2. Strangely, the manual for the MathPrint still insists that negative numbers be placed in parentheses to do temperature conversions. This is probably left over from the previous manual!

Technically, that should be considered a bug.

Operator precedence usually don't change, due to compatibility.

Priority goes down drastically, from above unary-minus, to below subtraction !
All that without an updated documentation.

[ijabbott]

(01-13-2019 09:11 PM)Albert Chan Wrote:  

(01-13-2019 07:28 PM)ijabbott Wrote:  In the new TI-30X Pro MathPrint, unit conversions seem to have a much lower priority, so that '-1 °C⯈°F' and '2-3 °C⯈°F' both produce a result of 30.2. Strangely, the manual for the MathPrint still insists that negative numbers be placed in parentheses to do temperature conversions. This is probably left over from the previous manual!

Technically, that should be considered a bug.

It's more consistent now. The order of operations table in the manual did include conversions, but only for things like fraction to decimal conversions. It never mentioned unit conversions in this table.

The manual for the new calculator doesn't mention unit conversions in the order of operations either, but they seem to have the same or similar priority to other conversions as far as I can tell.

Quote:Operator precedence usually don't change, due to compatibility.

Priority goes down drastically, from above unary-minus, to below subtraction !
All that without an updated documentation.

There are other changes to the order of operations, so I guess full compatibility with the old calculator wasn't much of a concern. Fractions have moved to a higher priority. Also bitwise logic operators and the STO→ operator have been added to the table, but only because they were absent before, and I don't think those have actually changed priority.

[lrdheat]

The TI-30X Pro MathPrint is decidedly better than the CASIO 991EX at handling improper integrals. Success with int (1/5root (1-x) ) from 0-33 =~-18.75, int 1/(2root(4-x^2) from 0-2 =~1.57 (pi/2). CASIO generates math error.

[Eddie W. Shore]

I tested four improper integrals recently (after the substituting x = tan(theta) and dx = d(theta)/cos^theta), and the TI-36X Pro handled all four of them.

[lrdheat]

Of course, on the CASIO, a usually excellent approximation is obtained by dividing integral into 2 integrals integrated over intervals 1 E-12 away from the undefined point (occasionally, a larger departure than 1E-12 is necessary).

True, improper integrals were handled by the 36X...not as quickly...

[ijabbott]

I've done a few speed comparisons between the TI-30X Pro MathPrint, the TI-36X Pro (or TI-30X Pro MultiView), and one of their greatest rivals, the Casio fx-991EX ClassWiz.

For a measurement technique, I basically filmed the calculations on my phone and measured the time using video editing software. There is a little bit of wiggle room because the calculator screens take some time to refresh, but I estimate my timings to be accurate to about ±0.1s.

Test 1 - classic summation based benchmark

This is the classic summation based benchmark from http://www.hpmuseum.org/forum/thread-9750.html with n=1000.
\[ \sum_{x=1}^{1000} \sqrt[3]{e^{\sin(\tan^{-1}(x))}} \\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 103.7 \\
\text{TI-36X Pro} & 257.9 \\
\text{Casio fx-991EX} & 106.9
\end{array} \]

Test 2 - Eddie Shore's \(x^{-2}\) summation test

This is a summation test from Eddie's speed test video: https://youtu.be/39tcSQBakMo?t=156
\[ \sum_{x=1}^{500} x^{-2} \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 19.6 \\
\text{TI-36X Pro} & 37.4 \\
\text{Casio fx-991EX} & 22.4
\end{array} \]

Test 3 - Eddie Shore's numeric solver test

This is a numeric solver test from Eddie's speed test video: https://youtu.be/39tcSQBakMo?t=109
\[ \text{Solve}\ e^x + .2x^3 = 3\ \text{for}\ x \text{.} \\
\text{Initial guess:}\ x=10 \text{.} \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 1.7 \\
\text{TI-36X Pro} & 5.5 \\
\text{Casio fx-991EX} & 1.6
\end{array} \]

Test 4 - Eddie Shore's \( \frac{\sin(x)}{x} \) integration test

This is an integration test from Eddie's speed test video: https://youtu.be/39tcSQBakMo?t=11

Note that the actual test that Eddie ran (and repeated by me) has a different upper limit than that shown on the slide.
\[ \int_{.001}^{.6} \frac{\sin(x)}{x} dx \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 0.9 \\
\text{TI-36X Pro} & 3.0 \\
\text{Casio fx-991EX} & 0.9
\end{array} \]

Test 5 - Eddie Shore's \( e^{-x} \) integration test

This is another integration test from Eddie's speed test video: https://youtu.be/39tcSQBakMo?t=38
\[ \int_0^{100} e^{-x} dx \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 2.5 \\
\text{TI-36X Pro} & 5.7 \\
\text{Casio fx-991EX} & 3.4
\end{array} \]

Test 6 - VBlogMag's \( e^{x^3} \) integration test

This is an integration test from VBlogMag's calculator benchmark video: https://youtu.be/DHRsvSTGiBc?t=584
\[ \int_0^6 e^{x^3} dx \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 8.6 \\
\text{TI-36X Pro} & 89.3 \\
\text{Casio fx-991EX} & 24.4
\end{array} \]

Conclusion

On the whole, the TI-30X Pro MathPrint is significantly faster than its predecessor (as expected), and slightly faster than the rival Casio fx-991EX in most tests. The result from VBlogMag's integration test has a surprisingly fast time for the TI-30X Pro MathPrint (compared to the other two calculators), but I double checked it. (The TI integration tests were performed using their default epsilon setting.)

[lrdheat]

Thanks, Eddie!

Note on the six(x)/x integral, the TI's allow the integration interval to begin with zero.

TI's allow integration of max( sin x,cos x) as an example. Also, product is available in addition to summation, lcd, gcm also available on the TI's.

Have you run into a limit on characters available to enter? It appears to be more forgiving than the 36X Pro, although I haven't really tried to reach it limit.

[ijabbott]

(01-19-2019 10:19 PM)lrdheat Wrote:  Have you run into a limit on characters available to enter? It appears to be more forgiving than the 36X Pro, although I haven't really tried to reach it limit.

It's about 25% larger. I managed to enter 101 characters (mostly digits with a '+' every 10th character) on the MathPrint compared to 80 characters on the older model.

[lrdheat]

Thanks!

If I remember correctly, the 36X could do 80 characters in classic mode, but only 40 in MathPrint. 100 characters should handle most problems...

[lrdheat]

MathPrint seems to admit 40 to 47 characters, depending on the application (36X). The 36X had a limit of just 41 trials for binomial distributions. I just tried 1000 trials on the 30X Pro MathPrint, and it was allowed!

The 991EX returns random numbers of only 3 digits. The 30X Pro MathPrint returns 9 digits. Same with the 36X Pro.

[lrdheat]

The TI's can calculate prime factors of 6 digit numbers. The 991EX can admit 8 digit numbers.

[pier4r]

(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: https://youtu.be/DHRsvSTGiBc?t=584
\[ \int_0^6 e^{x^3} dx \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 8.6 \\
\text{TI-36X Pro} & 89.3 \\
\text{Casio fx-991EX} & 24.4
\end{array} \]
[/align]

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

[ijabbott]

(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: https://youtu.be/DHRsvSTGiBc?t=584
\[ \int_0^6 e^{x^3} dx \\
\\
\begin{array}{c|r}
\text{Model} & \text{Time (s)} \\
\hline
\text{TI-30X Pro MP} & 8.6 \\
\text{TI-36X Pro} & 89.3 \\
\text{Casio fx-991EX} & 24.4
\end{array} \]

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

Thanks!

I'm a bit puzzled why my time for my TI-36X Pro was about 19 seconds shorter than VBlogMag's (real name Martin Lorton). I know his calculator is older than mine since the video is from Feb 2014 and my TI-36X Pro has a 2015 manufacturing code (L-0315B - Kinpo Philippines, March 2015, revision B), so perhaps they increased the speed or improved the algorithm a bit. (I also have a TI-30X Pro MultiView (same as a TI-36X Pro) with a 2016 manufacturing code L-0416B. That is more or less the same speed as my TI-36X Pro - less than a second faster on this test. I can put that slight difference down to oscillator tolerances.)

[pier4r]

VBlogMag got also some setups messed up (50g). It happens often on youtubers that wants to cover too much with too little time.
Or also when they do not realize subtleties. Like comparing programming environments and the fact that if the algorithm is different on two machines, it is not really a good comparison.
Or also on the integral test, it depends with which precision one works. With my sharp el 506w I can decide the subdivision interval and it can get from very quick and imprecise to very slow and precise.

I understand that is better for viewers to keep it simple. But ok one could create "response" videos to refute some approaches.

edit: also it is x^3 not x^2 as you wrote in latex. Maybe is that the speed up reason?

[Benjer]

I have a TI36X Pro with manufacturing code L-0516. In Mathprint mode it does VBlogMag's integration in about 82 seconds. In classic mode it does the same in about 36 seconds. I did a few runs in each mode and the results were consistent. I was getting the same answer he was getting so I'm assuming it's the same function his was.

Not sure why the TI gives different performances based on display mode. I did not see a similar phenomenon on the Casio.

[lrdheat]

Same sort of speed up on the 30X Pro MathPrint...int(abs(sin x)/x) over interval -pi/4 to pi/3 takes ~28 seconds in MathPrint mode, ~19 seconds in classic mode (default epsilon).

[lrdheat]

When following Thomas Klemm's advice, (diving integral into 2 parts...-pi/4 to 0 plus from 0 to pi/3), in MathPrint, the TI 30X Pro MathPrint was Night and day faster at <3 seconds!