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### Benchmark test e^x^3

Posted: Sun Feb 10, 2019 9:12 pm
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.

https://www.youtube.com/watch?v=DHRsvSTGiBc

I used this test for several other calculators (it takes about 4 seconds for the new Casio CG50 to accomplish this task, several smaller scientific calculators need more than 1 minute) and tried some variants for larger calculators:

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).

I was astonished, that the HP Prime could calculate the intervall of e^x^3 only between 0 and 8,9 - the result being 6,14 E303. This is still the case with the newest firmware release. It should be able to do the same as the HP 50G because the limit is also E499. Why does it fail?

The TI NSpire can calculate the intervall of e^x^3 between 0 and 13 (result: 2,75 E951) quite fast. It's limit is E999.

How long does it take for the DM 42 to caculate the intervall of e^x^3 between 0 and 6? Is it as fast as the HP Prime or TI NSpire?
Can the intervall of e^x^3 between 0 and 22 be calculated with the DM 42?
The result should be 2,81 E6000 (that is the result shown by https://matheguru.com/rechner/integral).
How long does it take to calculate this interval?

### Re: Benchmark test e^x^3

Posted: Sun Feb 10, 2019 10:06 pm
On the DM42 on battery power (so, the slow mode):

For interval of 0..6 => about 2-3 seconds
For interval of 0..13 => about 11-12 seconds.
For interval of 0..22 => about 22-23 seconds (value=1.61E4621)

So, pretty quick!

Edit after more posts): Eps used was 1E-06

### Re: Benchmark test e^x^3

Posted: Sun Feb 10, 2019 10:57 pm
Beginner wrote:
Sun Feb 10, 2019 9:12 pm
The TI NSpire can calculate the intervall of e^x^3 between 0 and 13 (result: 2,75 E951) quite fast. It's limit is E999.
How fast is "quite fast"? Just for curiousity ...

### Re: Benchmark test e^x^3

Posted: Mon Feb 11, 2019 9:47 am
Some more data:

On battery (Accuracy factor = 0.01):

0..6 = 5.9640E91 (<2 s)
0..13 = 2.7549E951 (<4 s)
0..22 = 1.6059E4621 (<9 s)
0..24 = 2.8145E6000 (<9 s)
0..25 = Out of range

On USB (Accuracy factor = 0.01):

0..6 = 5.9640E91 (<1 s)
0..13 = 2.7549E951 (<2 s)
0..22 = 1.6059E4621 (<3 s)
0..24 = 2.8145E6000 (<3 s)
0..25 = Out of range

Accuracy factor (On USB):

0..24 (acc=1) = 3.638951888E5803 (<1 s)
0..24 (acc=0.1) = 2.809107013E6000 (<2 s)
0..24 (acc=0.01) = 2.814494035E6000 (<3 s)
0..24 (acc=0.001) = 2.814459733E6000 (<6 s)
0..24 (acc=0.0001) = 2.814459733E6000 (<6 s)
0..24 (acc=0.00001) = 2.814459726E6000 (<12 s)
0..24 (acc=0.000001) = 2.814459726E6000 (<12 s)
0..24 (acc=1E-10) = 2.814459726E6000 (<23 s) More digits: 2.814459725921252477432075662808156
0..24 (acc=1E-20) = (Stuck in a loop) Edit: Actually I did not had the patience to wait enough, it is not looping, it takes around 6 minutes. Final result: 2.814459725921296162203929219415341E6000

In comparison with Wolfram result:
2.8144597259212961622039292556760324066E6000
2.814459725921296162203929219415341E6000

### Re: Benchmark test e^x^3

Posted: Mon Feb 11, 2019 2:55 pm
@ Walter:

The TI NSpire needs about 2 Sec for the calculation.

### Re: Benchmark test e^x^3

Posted: Mon Feb 11, 2019 2:57 pm
@ StreakyCobra

Thanks a lot!