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Sharp EL-W506T vs. Sharp EL-W516T
11-10-2019, 11:14 AM
Post: #1
Sharp EL-W506T vs. Sharp EL-W516T
What is the difference between the Sharp EL-W506T and the Sharp EL-W516T?
I am trying to figure out what the top of the line Sharp non-programmable non-graphing scientific calculator is so I can compare it with the Hewlett Packard HP-35S, Casio fx-991EX and Texas Instruments TI-36X Pro.
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11-10-2019, 02:15 PM
Post: #2
RE: Sharp EL-W506T vs. Sharp EL-W516T
(11-10-2019 11:14 AM)Guy Macon Wrote:  What is the difference between the Sharp EL-W506T and the Sharp EL-W516T?
I am trying to figure out what the top of the line Sharp non-programmable non-graphing scientific calculator is so I can compare it with the Hewlett Packard HP-35S, Casio fx-991EX and Texas Instruments TI-36X Pro.

It appears the EL-506T is newer, though I can't say what the difference is between them.

The Sharp website lists the EL-W506T and not the 516, and is current as of September '19

--Bob Prosperi
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11-10-2019, 04:14 PM
Post: #3
RE: Sharp EL-W506T vs. Sharp EL-W516T
Complicating the comparison is the different versions offered in different countries. The TI 30X Pro MathPrint, offered in Europe, is a faster version of the 36X Pro offered in the U.S. The European version accepts equations with a larger number of characters than the 36X Pro as well, offers stats for 50 lines of data. The CASIO 991 EX has various versions that offer slightly different function sets as well. The biggest difference to me between the CASIO’s and TI’s is CASIO loses history when turned off, and TI allows functions to be placed in f1 and f2, allowing for use elsewhere in the calculator such as in integration or other analysis. The 991EX requires the function to be rewritten for each use elsewhere in the calculator. The 991 EX can accept longer lists for statistical work, but loses this data upon turning unit off.
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11-10-2019, 05:18 PM (This post was last modified: 11-10-2019 05:19 PM by Guy Macon.)
Post: #4
RE: Sharp EL-W506T vs. Sharp EL-W516T
(11-10-2019 02:15 PM)rprosperi Wrote:  It appears the EL-506T is newer, though I can't say what the difference is between them.

The Sharp website lists the EL-W506T and not the 516, and is current as of September '19

Hmmm. I just tried shopping for one, and all the vendors (not just Amazon, but a bunch of different sites found with Google shopping) either show this:

https://www.amazon.com/dp/B078WRWS6Q/

https://images-na.ssl-images-amazon.com/...L._AC_.jpg

or this:

https://www.amazon.com/dp/B06XKLKNX9/

https://images-na.ssl-images-amazon.com/...L1500_.jpg

...which, of course, contradicts the Sharp website:

http://www.sharp-calculators.com/en/cont...6-el-w506t

I am holding in my hand a calculator that says "Sharp EL-W516T" on the front and Sharp EL-W516TB-SL (The BSL means "black slimline") on the blister pack. I checked very carefully and it is 100% identical with the EL-W506T Sharp shows on the website except for the model number, and advertises the same 640 functions.

Arrrgh! Why do calculator manufacturers DO this??
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11-10-2019, 05:57 PM
Post: #5
RE: Sharp EL-W506T vs. Sharp EL-W516T
Good question. I sometimes have a hard time keeping the Casio scientific calculators apart.

I think the 516 and 506 are similar and both have calculus functions.
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11-10-2019, 07:50 PM
Post: #6
RE: Sharp EL-W506T vs. Sharp EL-W516T
All the Sharp EL-Wnnn... utilize the "WriteView" feature, which is marketing speak for displaying algebraic equations in 'graphical' form (meaning fraction, integral and root symbols, etc. not true graphics). Models that don't have the 'W' prefix in the model don't have that capability. Most often (but not 100% of the time) the trailing letters are for colors, cover stle, and other pkg. type tweaks.

--Bob Prosperi
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11-10-2019, 08:10 PM (This post was last modified: 11-10-2019 08:13 PM by ijabbott.)
Post: #7
RE: Sharp EL-W506T vs. Sharp EL-W516T
I guess there are just minor regional differences between the EL-W516T (chiefly North America) and EL-W506T (chiefly Europe and rest of the world). Similar to the situation with Casio fx-115ES Plus versus fx-991ES Plus.

— Ian Abbott
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11-12-2019, 02:47 AM
Post: #8
RE: Sharp EL-W506T vs. Sharp EL-W516T
My first post here, but it seems hard to find a good active forum for chatting about calculators and this seems to be pretty active. I mostly mess around with Casio & Sharp as they seem to be plenty good enough for my purpose at the moment, but I do have an HP49G+ (which I am horrid at using, I did a few tutorials on RPN and I do like it, but I can't seem to help accidentally clearing the stack all the time), although as I gain a bit more mathematical knowledge I'll have to revisit using that again.

Hopefully doesn't get flagged as spam, but I think it's likely the EL-W506T & EL-W516T are identical much like the EL-W506X & EL-W516X that came before. There is room for doubt, but the product guide (Page 32) on Sharp's website list the EL-W506T as having 640 functions which from what I can see is the same as the Sharp EL-W516T.

Here is a link to that product guide as well as some other useful stuff, though it is easy enough to google:
http://www.sharp-calculators.com/en/cont...-downloads

I'll recommend grabbing the Operational guide for the EL-W506T as this has a bit more detail then the bundled instruction manual. There are still some holes though; for example I hear complaints with the Sharp's constant 'k' ability which is only mentioned in passing. Check out https://global.sharp/contents/calculator...index.html for a better idea of what causes 'k' to appear.

Even has an emulator for the EL-W506T (no apparent time limit like the Casio emulators).

It's worth noting that the EL-W506T loses the 4 formula storage memories. Personally I think that is a rather understated downgrade, as the amount of lines stored in multi-line playback is dependent on the size of the formulas and numbers entered. For example this equation will only allow about 2 lines of multi-line playback (everything to the right of the integral, the left is just the Sharp equivalent to the right (The Sharp EL-W506X/T uses the Simpson algorithm for estimating definite integrals):

[Image: fkU1r5o.png]

b = upper limit, a = lower limit, d = number of double divisions to use for the interval (Simpson's needs to have divisions that are multiples of 2, so if d=64, we actually break up the graph into 128 chunks to calculate the area).

When dealing with big formula's the last thing you want to be doing is retyping in them, so if you want to use that formula again, you need to keep scrolling up to run the equation to make sure it stays in memory. Being able to store 4 big equations like these completely removes any apprehension of accidentally pushing your formula off the multi-line 'stack'.

Looking at the manual, the buffer is about 159 characters, so since this equation is pretty close to that limit, 2 entries matches up with the 340 characters or so quoted for multi-line playback for the EL-W506X/516X. With 4 function memories that extends the effective memory close to a thousand.

That being said, the implementation of the table function on the EL-W506T is very well done, it just calculates as it goes, so there is no limit to what you can view, set the starting interval, interval size and away you go. I recommend giving the emulator a whirl to see how it works.
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11-13-2019, 06:27 PM
Post: #9
RE: Sharp EL-W506T vs. Sharp EL-W516T
My daughter had to buy an EL-W506X for her math course at school. This is essentially a W506T without WriteView. When she allowed me to play with it I tried one of my standard tests, the definite integral int(0, 6, exp(x^3),x). The result came up quite fast but was way off (the fx-991DE is dead on btw.).
I was curious about the algorithm they implemented and found, they use Simpson's formula but would never calculate more than n=100 intervals. No matter the precision needed or fixed digits.
This makes it rather unreliable when used for integrals.
Patrick
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11-13-2019, 11:43 PM
Post: #10
RE: Sharp EL-W506T vs. Sharp EL-W516T
(11-13-2019 06:27 PM)Pjwum Wrote:  This makes it rather unreliable when used for integrals.

Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. Smile.

Don't get me wrong, I do it too, but never mistake that sort of recreation with real-world problems, especially in High School.

Also, the EL-W506X does indeed have WriteView, it says it right on the face of the calculator above the LCD. As noted above, the "W" in all the EL-Wxxx models means that they do have WriteView. Maybe you meant the EL-506X, which indeed does not have WriteView.

--Bob Prosperi
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Yesterday, 03:53 AM
Post: #11
RE: Sharp EL-W506T vs. Sharp EL-W516T
The Sharp EL-W516x (and presumably the newer EL-W506T) seems to handle a pretty big number of divisions though; I tried a division count of 131,072 which worked fine, although you are probably going to want to go up the road and purchase some biscuits and boil the jug while you wait.

I'm guessing you meant the EL-506X, in which case I agree that being limited to n=100 seems pretty small unless you are dealing with small changes in area. The Casio fx-570MS, which also uses the Simpson method, can handle up to 2^n where you can choose a maximum value of n=9, or 512 divisions which is significantly better.

I'm off now on a Tangent about the Casio MS series, so please skip if uninterested!:
What though impresses me especially about the Casio MS series integration (despite not being as flash as the ES & EX series with it's faster and more accurate integration algorithm) is that it truncates the integration result to a certain number of significant figures depending on the number of the divisions and the function.

It really seems to be truncating the uncertain digits based on an internal error range calculation, but I find it hard to believe it uses the Simpson's rule error function since it requires calculating the 4th derivative of the function first and finding it's maximum....I mean if it was really calculating the error function, that is more impressive then taking the integral as far as I'm concerned Big Grin

Simpson Error function is |Es| at the bottom of this linked page: http://tutorial.math.lamar.edu/Classes/C...grals.aspx

You can see this error function at work, take the function e^x (done on Casio fx-82MS temporarily upgraded to fx-570MS):

Interval [0,1]:
integrate(e^x,0,1,n=4) = 1.71828
integrate(e^x,0,1,n=6) = 1.71828183

Interval [0,2]
integrate(e^x,0,2,n=4) = 6.389
integrate(e^x,0,2,n=6) = 6.389056

With the Simpson error function it is always taking the absolute maximum of the 4th derivative, so by extending the interval to 2, we get a steeper interval and so higher maximum error (ie e^x when x=2, and since the derivative of e^x is just e^x, so will it's forth derivative be). This seems to be what is happening in the above examples, which explains why you have less digits over the larger interval despite using the same number of divisions. Regardless of how they did it, it amazes me that they managed to pull it off on a calculator that doesn't even have natural textbook entry.

In addition, if the confidence is too low it will throw a math error:
integrate(e^x,0,0.1,n=1) = 0.1052 (Casio auto-algorithm logic selects n=3)
integrate(e^x,0,1,n=1) = 2 (Casio auto-algorithm logic selects n=3)
integrate(e^x,0,2,n=1) = Math Error (Casio auto-algorithm logic selects n=5)

I can't say for certain what error checking algorithm is being used, but as long as the estimate gives an equivalent or higher error range back it means you can count on the digits you see. From a bit of testing:

integrate(e^(x^2),0,5):
Wolfram answer: 7,354,153,747.83713

64 Divisions:
Casio: 7,000,000,000
Sharp: 7,368,738,187
|Es| <= 26,106,748.11

Adding the error in the actual result is somewhere between:
7,342,631,439 - 7,394,844,935

The first 2 significant figures could be either 73 or 74 so the Casio gave the correct result back as you can rely only on the first significant figure.

512 Divisions:
Casio: 7,354,200,000
Sharp: 7,354,157,599
|Es|<= 796.7147252
7,354,156,803 - 7,354,158,396
Looks like the first 6 significant figures can be counted on with rounding: 735416. The Casio could of gone for another significant figure, but it still returns the correct answer.

Note: that |Es| gives the maximum possible error for a function using the Simpson rule given the number of divisions, and it's 4th derivative; not the actual error.

In addition it seems to automatically vary the number of divisions depending on the function and it's interval, so certain integrations will go faster. This is something Sharp needs themselves if they are sticking with the Simpson method (both the error and auto interval logic).

I guess with the ES and now EX series stealing the show from the MS with it's better integration algorithm (Gauss-Kronrod?, it's above my current math ability) and nicer display it probably doesn't matter anymore, but this is a rather impressive feat IMO. I also like that the MS is still the only series with the "Copy-Replay" function, or the ability to scroll up several functions ago and copy that function and all others that proceed for editing.

Look at me blabbing on about the Casio MS series on a post about a new Sharp.

Back to the Sharp:

I still prefer my Sharp EL-W516X over the Casio fx-115es Plus (only by a tiny bit, as I much prefer the equation solver, Integration and differentiation on the Casio), but mostly because of these 3 reasons:
1) The ability to save your Writeview history when powering off.

2) Being able to store relatively big equations in 4 memories and easily recall them (eg the |Es| error tests were done on the Sharp, since I can store both the 4th derivative maximum, the |Es| function to make use of that, as well as the Summation version of the function (though I could just of used the built in Sharp one!)).

3) Great Summation functionality, since you can specify the interval size (algebraically as well).

If it was the Casio fx-991ex instead, well, I'd probably go with that for it's much better display and faster processing, but I would miss terribly the ability to save my calculation history or formulas.
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Yesterday, 06:35 PM (This post was last modified: Yesterday 09:08 PM by Pjwum.)
Post: #12
RE: Sharp EL-W506T vs. Sharp EL-W516T
(11-13-2019 11:43 PM)rprosperi Wrote:  Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. Smile.

I checked and yes, it is an EL-W506X and it says WriteView right over the LCD.

Let me come back to its calculus capabilities. I repeated the integral and these are the numbers:
Casio fx-991DE: 5.963938092E+91
Prime (Handheld): 5.96393809188E+91
Sharp W506X: 7.466216848E+91

Meanwhile I learned you may specify n as an option when entering the formula.

But does its auto mode of only 100 Simpson intervals really affect everyday calculations? Let us assume some average physics teacher in high school proposing this task: Calculate the energy needed to bring Tesla's starman (1000 kg) one light year away from Earth!
Instead of finding the antiderivative you try to solve the integral(rE, 1 ly, G*mE*1000kg/r^2) numerically. In auto mode without specifying n you will then find (kg*m^2/s^2):
Casio fx-991DE: 6.251161691E+13
Prime (Handheld): 6.25116169124E+13
Sharp W506X: 1.547252475E+20
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Yesterday, 11:22 PM
Post: #13
RE: Sharp EL-W506T vs. Sharp EL-W516T
(Yesterday 06:35 PM)Pjwum Wrote:  
(11-13-2019 11:43 PM)rprosperi Wrote:  Though probably just perfect for any integral your daughter will encounter... and likely anyone else that doesn't seek pathological equations to integrate. Smile.

I checked and yes, it is an EL-W506X and it says WriteView right over the LCD.

Let me come back to its calculus capabilities. I repeated the integral and these are the numbers:
Casio fx-991DE: 5.963938092E+91
Prime (Handheld): 5.96393809188E+91
Sharp W506X: 7.466216848E+91

Meanwhile I learned you may specify n as an option when entering the formula.

But does its auto mode of only 100 Simpson intervals really affect everyday calculations? Let us assume some average physics teacher in high school proposing this task: Calculate the energy needed to bring Tesla's starman (1000 kg) one light year away from Earth!
Instead of finding the antiderivative you try to solve the integral(rE, 1 ly, G*mE*1000kg/r^2) numerically. In auto mode without specifying n you will then find (kg*m^2/s^2):
Casio fx-991DE: 6.251161691E+13
Prime (Handheld): 6.25116169124E+13
Sharp W506X: 1.547252475E+20

Gee, that's only off by a factor of ~2.5E06; what's 1.5E20 kg*m^2/s^2 among friends? Wink

Seriously, that is surprisingly poor, so you've made a really good point here, though I still doubt she will get an assignment like that in High School.

If you set n manually, is it retained for future integrals, or is it reset to the default for each integral/equation you try to solve?

From curiosity, do you happen to know how many intervals the fx-991DE and Prime used to achieve essentially the same result?

--Bob Prosperi
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Today, 01:50 AM (This post was last modified: Today 01:55 AM by Mjim.)
Post: #14
RE: Sharp EL-W506T vs. Sharp EL-W516T
I tried this myself, but I kept getting different results. I downloaded Xcas to my PC (https://www-fourier.ujf-grenoble.fr/~parisse/giac.html I think the same engine behind the HP Prime):

Using: G=6.67430*10^-11, rE = 6.371*10^6, mE = 5.972*10^24, 1ly (in metres) = 299,792,458*3600*24*365.25
C = G*mE*1000 = 3.98589*10^17

E = integrate(C/r^2, rE, 1ly):
Wolfram (only gave 6 significant figures): 6.25631*10^10
Xcas: 6.25630506563*10^10
Casio fx-9750GII: 6.256305066*10^10
Casio fx-570MS (upgraded temporarily from a fx-82MS): Throws math error.
Sharp EL-W516X:
-Default divisions: 1.54840203*10^17
-1024 divisions: 6.694153651*10^10
-4096 divisions: 6.258289041*10^10
-32768 divisions: 6.251558833*10^10 (This took a very...very long time)

Not sure if these results are right; might of made a mistake with some units somewhere.

The Sharp is way off, part of it could be internal digit accuracy. If you move the constant C outside of the integral the Casio fx-9750GII will give 29390.80513 as an answer which will actually increase if we decrease the distance to 1 light second where it pops back up to 6.1233*10^10. The Xcas result is perfect either way, so perhaps the Prime will be similar?

The Casio fx-82MS error algorithm basically told us to go away, which is a better outcome since there is no way it could give a good approximation using the Simpson algorithm, if even the Sharp at 1024 divisions (512 more then the max on the Casio MS), couldn't even get a single significant figure down.

Good example for showing the weakness in the Simpson Integration algorithm. I have to agree that I don't trust the Sharp for integration, but to be fair, any calculator using the Simpson algorithm will likely have the same issue; the Casio 570MS just clearly recognizes when it won't be able to deliver a good result and throws a math error, but any other calculator with the same Simpson Algorithm will probably suffer similarly.

BTW, with this integration example, 1/r^p is convergent if p > 1; so since p = 2 we know that this function is convergent. The energy needed to offset earth's gravitational influence is essentially a fixed value beyond a certain distance. In any case, this means there isn't much difference between 1 light day and 1 light year in terms of energy required, which makes sense as earths gravity is pretty much negligible after traveling 173 AU or 173 times the distance from earth to the sun).
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Today, 07:45 AM
Post: #15
RE: Sharp EL-W506T vs. Sharp EL-W516T
According to the UG the Casio fx-991EX uses Gauss-Kronrod method.
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