Torture tests: what do they mean?

[Dieter]

(05-17-2014 08:20 AM)Tugdual Wrote:  please note that the 34s has a "double" precision mode.
I do get -7497258.185325587112905071814481370
Wolfram Alpha says that the result shall be
-7.497258185325587112905071831891248663417267943785263161571223470151837884956238​9571281869682281839570540842373435... × 10^6

So the 34s could achieve 26 digits.

As shown earlier, you generally cannot trust the last 8 digits. So 34–8 = 26 digits is the expected accuracy here. Likewise, the 32-digit Windows calculator returns -7497258,1853255871129050827752131, which is +1 unit in the 24th digit. Again, the last eight digits are off.

Now try Wolfram Alpha with the tangent of 355/226 rounded to 34-digits. This is what the 34s actually evaluates. You'll get tan(1,570796460176991150442477876106195) = -7497258,185325587112905071814481418... This agrees with the 34s result in 32 out of 34 digits.

Dieter