HHC 2015  Savage benchmark curiosity

10092015, 12:53 PM
Post: #7




RE: HHC 2015  Savage benchmark curiosity
(10092015 07:45 AM)Dieter Wrote:(10082015 08:31 PM)Claudio L. Wrote: Question still remains: why does it selfcorrect? There's a lot more than that going on! Take the first iteration, for example: 1470.99993303 LN EXP > 1470.99993302 (there's 1 change introduced here) ATAN TAN 1 + > 1471.99994304 1470.99991143 LN EXP > 1470.99991143 (but not on this path...) ATAN TAN 1 + > 1471.99992140 So deviations from the "exact" result happen somewhat randomly on both paths, sometimes it +/ 1 in the LN/EXP combo, sometimes it's +/1 in the ATAN function, which ends up around +/2e4 in the final result, amplified by TAN. By the time you get to iteration 1647, you've been following 2 different paths for 170 iterations, and you end up with 2 different numbers, both containing a number of random deviations in the last 4 digits. Magically, this iteration produces the exact same result, on both paths. The last position where the 2 paths differ has: 1647.99989715 and 1647.99992427 Applying the exact same operators to these 2 different numbers produces the exact same result... 1647.99989715 LN EXP > 1647.99989715 ATAN > 1.57018953072 1647.99992427 LN EXP > 1647.99992428 ATAN > 1.57018953072 Turns out that: tan(1.57018953071)=1647.99988358 tan(1.57018953072)=1647.99991074 tan(1.57018953073)=1647.99993790 This is a lot less magical than it appeared at the beginning (at least to me). All numbers between 1074 and 3790 in the last 4 digits will produce the same result. The difference 1e11 in the tangent produces +/ 2716 in the last 4 digits. If we think the last 4 digits are completely random, then there is a chance 2716 in 10000, or roughly 1 in 4, that they will produce the same result. That's a very good chance that the paths will get in sync again. I think the mystery is solved, the loop runs until these somewhat random errors produce values that are within the +/ 2716 in the last four digits, then the ATAN/TAN pair will coalesce these range of numbers into the same result, syncing back the paths. 

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Messages In This Thread 
HHC 2015  Savage benchmark curiosity  Claudio L.  10072015, 03:18 PM
RE: HHC 2015  Savage benchmark curiosity  Dieter  10072015, 07:37 PM
RE: HHC 2015  Savage benchmark curiosity  Claudio L.  10082015, 12:34 PM
RE: HHC 2015  Savage benchmark curiosity  Dieter  10082015, 07:11 PM
RE: HHC 2015  Savage benchmark curiosity  Claudio L.  10082015, 08:31 PM
RE: HHC 2015  Savage benchmark curiosity  Dieter  10092015, 07:45 AM
RE: HHC 2015  Savage benchmark curiosity  Claudio L.  10092015 12:53 PM
RE: HHC 2015  Savage benchmark curiosity  Dieter  10092015, 07:47 PM
RE: HHC 2015  Savage benchmark curiosity  Rodger Rosenbaum  11032015, 05:19 PM
RE: HHC 2015  Savage benchmark curiosity  Claudio L.  11052015, 02:18 AM

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