On 10/18, Jeff Law wrote: > On 10/17/18 4:21 PM, Giuliano Augusto Faulin Belinassi wrote: > > Oh, please note that the error that I'm talking about is the > > comparison with the result obtained before and after the > > simplification. It is possible that the result obtained after the > > simplification be more precise when compared to an arbitrary precise > > value (example, a 30 digits precise approximation). Well, I will try > > check that. > That would be helpful. Obviously if we're getting more precise, then > that's a good thing :-) > > jeff
Well, I compared the results before and after the simplifications with a 512-bit precise mpfr value. Unfortunately, I found that sometimes the error is very noticeable :-( . For example, using floats and comparing with a 512 precision mpfr calculation with input : = 9.99966979026794433593750000000000000000000000000000e-01 cosh: before : = 1.23053413391113281250000000000000000000000000000000e+02 cosh: after : = 1.23052398681640625000000000000000000000000000000000e+02 cosh: mpfr512: = 1.23053409952258504358633865742873246642102963529577e+02 error before : = 3.43885477689136613425712675335789703647042270993727e-06 error after : = 1.01127061787935863386574287324664210296352957729006e-03 There are also some significant loss of precision with long doubles: with input : = 9.99999999999996799706237365912286918501195032149553e-01 cosh: before : = 1.24994262843556815705596818588674068450927734375000e+07 cosh: after : = 1.24994262843556715697559411637485027313232421875000e+07 cosh: mpfr512: = 1.24994262843556815704069193408098058772318248178348e+07 error before : = 1.52762518057600967860948619665184971612393688891101e-13 error after : = 1.00006509781770613031459085826303348150283876063111e-08 So yes, precision may be a problem here.
