A quick precision test

[Claudio L.]

(06-05-2014 10:09 PM)Paul Dale Wrote:  

(06-05-2014 09:08 PM)Claudio L. Wrote:  I've also checked with Wolfram Alpha, and... exact same number! (I checked up to 36 digits only, the others are left to the reader to compare...)

When I do this on Wolfram Alpha, which is usually my gold standard for accuracy I get the numbers I quoted. This is the query I used.

Quote:hint: Alpha won't give you more than the number of digits you input, so it will show only 5 digits unless you add lots of trailing zeros to the input argument.

It will if you ask for them


- Pauli

Huh? The result given by alpha is different if you ask "with 72 decimal digits" or if you add 36 trailing zeroes to the number.
I just did:
COS(1.57079632679489661923132169163975144) with 72 decimal digits
(I didn't know you could write that in "human words", that's cool! if it only gave good answers...)
And I also did
COS(1.57079632679489661923132169163975144000000000000000000000000000000000000) (36 zeroes, for a total of 72 decimal digits, so it should be the same...right?)

The result in each case is:
2.098584699687552910487393316601323231×10^-36
2.09858469968755291048747229615390820 × 10^-36

What's going on? is it making the digits up or what? The second answer agrees with newRPL and preccalc, which is why I "conveniently" choose to believe that one. I say "conveniently" because it agrees with my code, not because I know it for a fact to be correct.

I used to trust the results from Alpha blindly (and from the past few posts, I can tell you too). Now I just don't know what to believe, and neither should you from now on.

Claudio