HP35 exp(ln(x)) bug, a new number found. Message #1 Posted by Kiwi Geoff on 25 Aug 2010, 11:35 p.m.
The famous exp(ln(2.02)) bug on the original HP35 resulted in HP printing an Errata, part of which said:
" The numbers are 0.7030975114 and 0.995033085 x 10E2,
or integer multiples of the latter number through nine,
by itself, or when added to the former. "
I was curious as to whether there were any other numbers that
were not in the above "set" that would cause an incorrect answer
on the original HP35.
Doing a numerical search, I did find another number that does
not compute the exponential correctly on the original HP35.
exp(ln(1.12211)) = 1.111
After a little more number crunching, it seems the full list of original HP35 exp(ln(x)) errors are as follows. They all produce values that need to be multiplied by 1.01 to give the correct answer:
exp(ln(1.0201))
exp(ln(1.04060401))
exp(ln(1.12211))
exp(ln(2.02))
exp(ln(2.060602))
Only 5 numbers, from an astronomical number of correct results.
A true needle in a haystack problem.
For those who do not have an original HP35 (circa 1972) calculator, you can try the above numbers on this
HP35 Simulator.
If anyone can find more than the above 5 numbers  I would be very interested.
Story of the new number and the HP35 Errata.
Regards, Geoff Hitchcox (Christchurch, New Zealand).
