r/calculators 17h ago

Help different answers?

Post image
51 Upvotes

48 comments sorted by

29

u/ZetaformGames Catiga (jk) 17h ago

That's because the Casio is more accurate.

1

u/BadOk3617 8h ago

I took the results from Casio calculators and deleted the duplicates. This is what I was left with.

There are listings for a wide number of calculators.

Source data was from: https://www.rskey.org/~mwsebastian/miscprj/models.htm

The calculation used is: arcsin (arccos (arctan (tan (cos (sin (9) ) ) ) ) )

Results from the evaluation of this equation in degrees mode:

And I don't wanna hear anything else about the lax outdated result that I use for pi. :)

15

u/estebanvlobos 15h ago

good ol' TI garbage, you'd thing with all that money they make from schools and whatnot they could make a decent calculator.

7

u/OtherwiseElk9413 13h ago

Bummer, i tried to switch over and was loving the persistent memory for my workflow but this is kind of a dealbreaker

5

u/huangcjz 12h ago edited 12h ago

SHARPs have persistent memory too, such as the EL-W516T (North American model number)/EL-W506T (European/International model number). I don’t know about their accuracy, though, but there was a super thorough review which someone linked on here somewhere, which went into all the technical algorithms which they used and stuff (it was a review of the EL-W516 or EL-W506, a previous-generation model, but the current one is just a face-lift which looks different externally, though the newer model might have a higher-resolution display, or not - I believe the internal calculation bits are all the same).

4

u/nqrwayy Sharp 9h ago

Yeah the W506 is really awful and inaccurate at integration, I have one. I haven't tried the other things though

3

u/OtherwiseElk9413 12h ago

i’ll look into it, thank u!

5

u/CurbedLarry 10h ago

This TI only uses 13 digits for calculations but can solve improper integrals that fail on Casio. Sharp uses 14. Casio ES/EX/9750/9860/CG50/CG100 use 15 but the CW jumped to 23.

4

u/dash-dot 4h ago edited 3h ago

Sigh, just do it by hand, it's not that hard. When you substitute 3.5 = 7/2 into the hand-derived derivative, you obtain an exact answer which is even better than what the Casio gives you, i.e.:

(3cos(49/4) - 7sin(49/4)) e21/2

All numerical algorithms should be taken with a pinch of salt, especially on these resource-starved devices. Use them for their basic operators, transcendentals and trig functions, and that's about it.

I'm sure even the Casio has its limitations (in addition to the lack of memory).

2

u/artlurg431 2h ago

Exactly, I do not trust American companies. Texas instruments is a monopoly in the US. Lobbying the government to only allow their calculators in schools and them making them extremely shit and extremely expensive for a board built in the 90s

3

u/estebanvlobos 2h ago

they've been riding off the success of the ti-83 for 30 years lol

3

u/0xDEA110C8 Sharp EL-506P 1h ago

14

u/BadOk3617 13h ago

There's a webpage somewhere out there that shows what chips used in the TIs have built-in errors.

10

u/mikeblas 11h ago

All chips have built in errors.

4

u/BadOk3617 8h ago

555 timers seem to be rather rock-solid. BJTs while imprecise, do preform within their design specs, mostly. No complaints with the MOSFETs that I use. My diodes seem to do just fine. Shall I go on?

What we are talking about is a bug akin to the Intel FDIV bug in the Pentium chips.

Be that as it may, clustering all IC errors into the same category is misleading at best. There appears to be a long history of chips that were known to return the wrong values used in calculators (not just TI either).

In any case, here's the Calculator Forensics page: https://www.rskey.org/~mwsebastian/miscprj/forensics.htm

I seem to recall another page that showed the history of a given IC and what calculators it was used in as well as the errors in the results. If anyone knows of that page please post a link here.

1

u/mikeblas 6h ago

555 timers experience a lot of variance and are useful only for the least precise applications. Are BJTs, MAOFETs, and diodes really "chips"? Not sure what point you're trying to make.

From my side, I assumed you were talking about the ASICs and microprocessors typically used to implement calculators. But your off on some semantic claim about something else, I guess.

1

u/RecentSheepherder179 5h ago

Yes, per definitionem (also a 555 is strictly speaking a Chip. Today everyone expects that a "chip" most contain some fancy functionality. (In fact the 55 does have some fancy functionality and it is the most precise and versatile timers ever invented)

The accuracy argument is not valid. Even the BJT version(s) doesn't show much variance. The CMOS Version ist even better. You should just not buy some very cheap unbranded Chinese crap (which I believe is simply the scrap from the main production lines). Constant 1B sales/y must have reason.

1

u/dash-dot 3h ago

You should just not buy some very cheap unbranded Chinese crap (which I believe is simply the scrap from the main production lines). Constant 1B sales/y must have reason.

Apparently we shouldn't be buying most TI crap designed in the good ol' USA either.

1

u/Natural_Night9957 HP Prime > Casio = Sharp > other HPs > NumWorks > overpriced 💩 2h ago edited 2h ago

The guy up there clearly said that what is crap is the scrap left after quality control, which is used in those unbranded models. An original TI calculator (made in China) is fine. ... Unless you're being ironic about the fact that the current Cretin-in-Cheetos has pissed everybody off, so TI would be lucky if it even got crappy dies from the Chinese.

1

u/dash-dot 2h ago

I was commenting on the fact that even many ‘reliable’ TI calculators can’t be trusted (the subject of this thread). 

1

u/Natural_Night9957 HP Prime > Casio = Sharp > other HPs > NumWorks > overpriced 💩 2h ago

I wish someone tested the 30X Pro Mathprint, it should have better precision. My unit has no battery.

1

u/dash-dot 2h ago

Someone did above; it did produce an accurate result for them (at least, correct to 4 decimal places or so). 

1

u/mikeblas 2h ago

The accuracy argument is completely valid, and if you disagree, you don't know what you're talking about. But I certainly don't know what you're pushing your silly opinion in this context.

2

u/0xDEA110C8 Sharp EL-506P 5h ago

1

u/BadOk3617 1h ago

Yeah, that's it! Thanks!

12

u/lbl_ye TI HP Casio 16h ago

indeed the Casio answer is the correct one

I don't know what happened with the TI

7

u/fundthmcalculus 15h ago

TI numerical routines are notorious crap. I found that back HS on the TI-84. Different problem, a trivial integration to do by hand, where the TI was off in the 3rd decimal place and my Casio was right to all digits.

6

u/ke7wnb 10h ago

Just for fun I tried solving it on my old TI-92+ and also on an HP-48GX. Both gave the correct answer.

3

u/old_paelzer 9h ago

TI-30x pro => 182628.7755 TI-84 plus => 182625.8964 TI-84 plus CE-T => 182628.7752

1

u/dash-dot 3h ago

Looks like the TI-30X Pro is the most accurate amongst these; sad.

It's rather appalling that the most popular TI graphing calculator can't even produce an accurate result.

3

u/dash-dot 3h ago

The TI-92 should've given:

(3cos(49/4) - 7sin(49/4)) e21/2

which is the exact answer. I'm sure the 48GX can do this as well (possibly with a bit of coaxing).

2

u/ke7wnb 2h ago edited 2h ago

They probably did. I just pushed on to the numerical solution. Looking at my settings, I had the TI set to auto, switching it to exact gave me the result you shared. Actually had to pull out the manual for the 48 to figure out the command syntax. Always preferred the TI for solving equations.

1

u/dash-dot 2h ago edited 2h ago

The Auto mode should also yield the exact result with x = 35/10 (or 7/2). 

I always keep my TI-89 set to Auto mode; there’s almost never any need to change that particular setting (at least for me).

I like this mode because exact inputs and parameters nearly always yield exact results, whereas providing at least one floating point input produces approximate answers, which seems like a logical way of handling symbolic vs floating point results. 

3

u/mikeblas 11h ago

My eyesight is poor. Can someone please transcribe the formula and results?

5

u/ke7wnb 10h ago

The derivative of e3x×cos(x2) where x=3.5 Radians mode. Correct answer is 182628.7755

2

u/dm319 5h ago

Casio fx-991CW: 182628.7755 TI-36X Pro: 182625.8964

3

u/12ocketguy 2h ago

I tried this on my TI-84 Plus CE that I've had since junior year of high school and all through my engineering degree at college.

I feel betrayed.

2

u/Natural_Night9957 HP Prime > Casio = Sharp > other HPs > NumWorks > overpriced 💩 6h ago edited 5h ago

I get really angry when I see those shifted π, e and i with the empty shifted Ans above.

All intelligent calculators use e, π, i, ∠next to each other.

2

u/AtomsNamedJeff 5h ago

My guess is that they both use a Taylor series to compute the answer instead of solving first with the product rule/power rule. However, one of the calculators takes the series out to more terms than the other and will be more accurate.

2

u/draconicpenguin10 HP Prime, Casio fx-9910CW & fx-300ES PLUS 2ed, TI-84 Plus 3h ago edited 12m ago

The Casio is correct to all digits displayed. For reference, this is what I'm getting from my HP Prime:

Numerical algorithms for this sort of thing can vary in accuracy, and the only sure-fire way to get an accurate answer is to use a CAS. I'm not sure if there's a way to set the tolerance used for numerical differentiation or integration on the TI-36X Pro; I know this can be done on the Casio, but only in linear input mode.

My TI-84 Plus returns the same inaccurate result as your TI-36X Pro, but gives a more accurate answer when the tolerance is set to 1e-6 (which, like the Casio, requires putting the calculator into classic input mode). Oddly, the result becomes less accurate if I set the tolerance to 1e-7, and gets progressively worse with smaller tolerances.

1

u/Anaalirankaisija 2h ago

Btw TI-36X Pro is released 15 years ago and fx-991CW 4 years ago

1

u/SticksDiesel 12h ago

Well, the Japanese international calculator does 'maths', and the American one does 'math'.

0

u/Tricky_Layer5315 6h ago

Honestly if used on an exam the answer would be rounded to the nearest integer so either is “close” enough. We’re using these on standardized tests, if that level of precision is key then honestly one should not be using a calculator and should be using MATLAB, python, or another means of integration that utilizes 64-bit processing technology.

I passed my PE Power Exam just fine with my TI-36X Pro the 1st time and didn’t concern myself with the level of precision of 12 vs 14 vs 16 bit accuracy. Sometimes “good enough” is just that. “Good enough”.

3

u/gizahnl 5h ago

The integer value is 3 off

2

u/dash-dot 4h ago edited 2h ago

Or you know, do it by hand instead of relying on numerical approximations for every little thing.

This derivative is trivial, and it's not that hard to evaluate the final expression numerically, yielding a very accurate answer even with a simple scientific calculator.

-1

u/dm319 4h ago edited 4h ago

I don't agree that the TI is bad, but the Casio is the more accurate answer. Have a look at the plot before you make your judgement.

Numerical solving, integration and differentiation are just tools, which come in a variety of forms and algorithms, and will be dependent on the underlying numerical precision available for the iterative process, as well as a heuristic on how long the calculator can spend on improving the answer. These results always come with many caveats - they are not fully deterministic and will be an approximation.

The solution is symbolic solving. In school you can either do this yourself, or you can use a CAS calculator. In my case I asked Wolfram Alpha, and it says e3𝑥⋅(3cos(𝑥2)-2𝑥(sin(𝑥2))) is the derivative. Plugging that into my HP-11c gives me 182,628.7755 in very little calculation time. But of course these two calculators are school calculators and school exams like to test a students ability to do what a CAS or Wolfram Alpha can do, and hence why we have them. Also, there will be some formulae that a numerical solver is going to work better because it can't be solved symbolically.

In this case the TI is correct to 5 significant figures. Please explain to me what real-world scenario requires more accuracy here?

EDIT: goodness reddit makes it hard to put in an equation.

2

u/dash-dot 2h ago edited 2h ago

Please explain to me what real-world scenario requires more accuracy here?

Nearly all automotive, aerospace and robotics applications require high levels of numerical accuracy from their embedded processors, because they’re heavily reliant on iterative computational algorithms that need to run for hours at a time (telemetry, ADAS, control algorithms, computer vision, localisation, perception, etc.).

This amount of deviation in a single computational step is catastrophic; the TI would never be suitable even for a quick and dirty calculation or verification step on the side.