Online calculator simulators?

[jonmoore]

(07-10-2022 03:28 AM)pauln Wrote:  

(07-09-2022 09:17 PM)Albert Chan Wrote:  This has less to do with calculators, and more to do with math.

sin(9°) = sin(pi/20) ≈ pi/20
cos(sin(9°)°) ≈ cos(pi/20 * pi/180) ≈ 1 - (pi^2/3600)^2 / 2! ≈ 0.999996

We had lost 5+ digits precision, due to catastrophic cancellation.
That's why all calculator forensic test will lose 5 to 6 digits precisions.
This is true even if all calculations produce correctly rounded results!
[...]

This is a great observation. I have always found this test a little bit arbitrary and dubious, for the exact same reasons.

(It is a good test though to differentiate emulators from simulators.)

1 sin cos tan arctan arccos arcsin

in radians would have been a much better test.

My own take was that it has less to do with emulators vs simulators, but it does expose the under the hood math. Modern Casio's perform all calculations under the hood to 15 significant digits and they lose 6 digits of precision in this test. I was under the impression that HP's 50g and Prime also perform most calculations to 15 digits but this doesn't seem to be the case with trigonometric functions.

With Mathematica, I specified 14 significant digits via the NumberForm command and it also lost 6 digits of precision due to rounding error.

Albert's observation was indeed very good.

BTW if the test is performed with radians, all decent calculators resolve to 1 without any roundoff error. Looking forward to Alberts insight ref why roundoff error doesn't occur in with radians.