A quick precision test

[Paul Dale]

(06-06-2014 12:57 AM)Claudio L. Wrote:  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.

I'm very surprised by this too & I'm definitely going to be less trusting in the future. Can anyone try this out on mathematica?

I also use http://keisan.casio.com/ for high precision computations but it doesn't cope with these cases well.

The UNIX program bc is also capable of simple functions, although it can be slow. It gives at 1000 decimals:

Code:

.0000000000000000000000000000000000020985846996875529104874722961539\
08203143104499314017412671058533991074041716259787756261727399478831\
81185207919839671783270457963357452998367829339194961906347965703281\
47240869600249270055638757772742607382068677735487482252910132430921\
25011163621763952597207721771071265357158278110764553758510887962258\
51742560721740180609129907245224513459993921421070558798154580236042\
32407372510759903342617788153853840878295245182108915941345297357152\
95467887428299279732274687499923779112476604887692015658454432511395\
20186523310121703812758838897823845975508622927202662531025498360451\
74355215955818970707014736785295006140539706462425805627474361779111\
46786377286992186246904485553797769184501523663646490051717437459809\
22322920642489618488130423650012447886418342843748598070677109909502\
89199115883068012988455235118715782492326453234782257817862953771152\
40579453052914192224813788402907439508961163082003815873154380098742\
1749306835713073531394568393273816656830251173885

The digits don't change working to 10000 digits. The code is calculating cos(x) = sin(x + pi/2) and it is using 1.2 times the digits (1200 or 12000 respectively). As for, sin(x) it is using a Taylor series with a couple of additional digits.

This matches the values you're getting and your result from Wolfram.


- Pauli