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[HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL
01-03-2024, 10:42 AM
Post: #5
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL
Quote:By the way, what do you find for

The answer should be almost 33, and not infinity
as ERFc(33) =1.93206244519E-475).

I didn't implement erfc or its inverse function in the library so I have no result for comparison. But if you are interested in the correctness of your result, FriCAS gives


(3) -> digits 1000 

   (3)  5000
                                                        Type: PositiveInteger
(4) -> (1-erf 33.0)

  8_5649549993_550501983 E -474

And by comparing the result computed using higher precision (5000 digits), I think you can trust the above result up to the 7_7311393656 part.

Quote:inverse_erf(1E-9) =?

The correct answer should be about
8.86226925455E-10 (by effective integral execution)

IERF gives undefined result error, ERFIV gives 8.86226869911E-10.

I don't think FriCAS can do inverse ERF so I asked Wolfram, it says

8.8622692545275801388109740820522708507986498595507634336469 × 10^-10

(Wolfram computes the result in higher precision until the result converges, so I know all except the last digit can be trusted)
Given that nothing outside extended real number computation been used, I think the ERFIV gives pretty decent approximation.
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RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL - LdBeth - 01-03-2024 10:42 AM

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