Benchmark test e^x^3
02-13-2019, 07:34 AM
Post: #21
 Beginner Junior Member Posts: 19 Joined: May 2017
RE: Benchmark test e^x^3
Thank you for explaining the background. With the staggering improvements of the hardware from HP 50G via HP Prime G1 to HP Prime G2 is there any reason left for the limitations of the CAS?

If the HP 50G could do it, why should the HP Prime not be able to do it?

https://en.wikipedia.org/wiki/Comparison...alculators

512 KB RAM, 2 MB flash, expandable via 2 GB SD card (HP 50G)
32 MB RAM, 256 MB flash (HP Prime G1)
256 MB RAM, 512 MB flash (HP Prime G2)

Also the hardware of the DM42 seems to be much simpler than the hardware of the HP Prime G2. If an improved free version if the software of the HP 42s can do it, why should the "flagship" HP Prime G2 not be able to cope with the task?
02-13-2019, 09:32 AM (This post was last modified: 02-13-2019 09:37 AM by pier4r.)
Post: #22
 pier4r Senior Member Posts: 2,017 Joined: Nov 2014
RE: Benchmark test e^x^3
RAM and CPU are only elements you need to assemble on a PCB, whether you use them to the maximum is another story. Still already the task to design a PCB takes lots of efforts and testing.

Developing a sound math library takes a lot of effort. The 50g had the culmination of a math library that was developed over 20 years by several people concurrently. Porting the effort is not easy. The cas of the prime is a specific version of Giac/Xcas (n1). There may be scarcity of manpower or priority about the topic of large numbers.

On the dm42 they used the math engine free42 developed over tens of years by Thomas Okken (n2). It is not that sound math libraries/engines are developed overnight.

Then you should not forget the economical factor. People are paid in companies to generate profit (or at least not too big losses), they are not going to work on edge cases ( few people would actually care to compute a function with a result over e300).

For example you likely don't know that the prime list can handle only 10 000 elements, although there is plenty of ram available. Why? because likely the code to handle limited lists is more economical to maintain and the likelihood that people would exceed that limit is near zero.
Still one with a bit of work can create a library to handle lists of lists and easily exceed million of elements.

You can always contribute yourself for improvements with additional programs, and then you will also see how much effort it is needed. (but you will learn a lot!)
Or you can even sponsor HP directly with several hundred thousand dollars so they can fix what is important for you.

An observation: I see that youtubers with little knowledge of the calculators they use or math do more harm than good, also because they may be corrected but they don't fix their video that stays influencing people.

n1: https://www-fourier.ujf-grenoble.fr/~par...glish.html
n2: http://thomasokken.com/free42/history.html

Wikis are great, Contribute :)
02-14-2019, 10:15 PM
Post: #23
 Claudio L. Senior Member Posts: 1,671 Joined: Dec 2013
RE: Benchmark test e^x^3
(02-11-2019 03:28 PM)Beginner Wrote:  Some time ago I came across a youtube video in which as a benchmark test is suggested to calculate the intervall of e^x^3 between 0 and 6. The result is 5,96 E91. It takes about 1 second for the HP Prime, it takes more than 1 min for the HP 50G.

For the record, the 50g with newRPL can do this:
Code:
 'F(X)=EXP(X^3)' 0 6 1E80 NUMINT

The above is the numeric integral (NUMINT) of the expression, from 0 to 6 and with an acceptable error of 1e80 (hence we want 11 good digits since the result is of the order 1E91)
Gives the result in 3.7 seconds.

(02-11-2019 03:28 PM)Beginner Wrote:  It is possible to calculate the intervall of e^x^3 between 0 and 10,5 with the HP 50G (which takes several minutes but finally succeedes as expected, because the resultat is under E499 (2,22 E498).

Changing the upper limit to 10.5 and the tolerance to 1E488 (for 12 digits) takes newRPL 4.5 seconds. By the way, the correct answer is 1.701767227195E500, so I guess the stock 50g goes out of range after all. newRPL returns 1.701767227199E500, so the 12 requested digits are there.
02-15-2019, 02:30 PM
Post: #24
 Claudio L. Senior Member Posts: 1,671 Joined: Dec 2013
RE: Benchmark test e^x^3
(02-14-2019 10:15 PM)Claudio L. Wrote:
(02-11-2019 03:28 PM)Beginner Wrote:  Some time ago I came across a youtube video in which as a benchmark test is suggested to calculate the intervall of e^x^3 between 0 and 6. The result is 5,96 E91. It takes about 1 second for the HP Prime, it takes more than 1 min for the HP 50G.

For the record, the 50g with newRPL can do this:
Code:
 'F(X)=EXP(X^3)' 0 6 1E80 NUMINT

The above is the numeric integral (NUMINT) of the expression, from 0 to 6 and with an acceptable error of 1e80 (hence we want 11 good digits since the result is of the order 1E91)
Gives the result in 3.7 seconds.

(02-11-2019 03:28 PM)Beginner Wrote:  It is possible to calculate the intervall of e^x^3 between 0 and 10,5 with the HP 50G (which takes several minutes but finally succeedes as expected, because the resultat is under E499 (2,22 E498).

Changing the upper limit to 10.5 and the tolerance to 1E488 (for 12 digits) takes newRPL 4.5 seconds. By the way, the correct answer is 1.701767227195E500, so I guess the stock 50g goes out of range after all. newRPL returns 1.701767227199E500, so the 12 requested digits are there.

Update:
Setting precision to 16 digits (which makes sense if we only request 12 on the result, should've done this from the beginning), plus using a program << DUP DUP * * EXP >> instead of a symbolic expression results in a substantial speedup:
From 0 to 10.5 produces the result with 11 correct digits (lost one digit due to reduced precision) in 2.6 seconds.
From 0 to 6 with 12 correct digits in 2.15 seconds.

This is only to show that the 50g hardware is not *that* obsolete, its software is (coming from the HP28 OS the core math is much, much older).
02-15-2019, 10:20 PM
Post: #25
 Beginner Junior Member Posts: 19 Joined: May 2017
RE: Benchmark test e^x^3
Normally I use the "equation writer".

How do I have to prepare the HP 50G in order to use the code you described?

Do I have to modify the flags?

How do I start programming?
02-17-2019, 05:32 PM
Post: #26
 Beginner Junior Member Posts: 19 Joined: May 2017
RE: Benchmark test e^x^3