Benchmark test e^x^3

[Claudio L.]

(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).