Torture tests: what do they mean?

[Dieter]

(05-16-2014 09:18 AM)jebem Wrote:  Please check Dieter explanation, it makes all the sense to me.

Thank you very much. But let us not for get the most important thing here:

Quote:For me it is not about the number of digits in the display, it is about the number of internal digits used in approximate calculations.

It's all about the user. We should never forget that our calculators cannot do exact mathematics (except those with a CAS). All they do are numerical approximations. We always have to keep this in mind - and use our brains to get the most out of it.

A nice example has been discussed recently. It was about the term tan((0.5 – x)*pi) that was calculated within a WP34s function. This formula will return inaccurate results as x approaches zero, and finally the results will be completely meaningless as the tangent of the internal approximation of pi/2 is returned for any x below 5E–11, 5E–13, 5E–17 or 5E–35, depending on the number of available digits. So sooner or later this approach will fail. Now it's up to you, the user, to realize this danger of digit cancellation and use your mathematical knowlegde: rewrite the expression as cot(pi*x) and everything works fine even for the lowest x the calculator can handle. Use this for any x below 0.1 and the original formula for all others, and you'll get a correct answer.

In other words: any calculator is just as good as its user allows it. It's the same story as with any other tool. ;-)

Dieter