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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
inverse_ERFc(1.93206244519E-475)?

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

Code:

(3) -> digits 1000 

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

   (4)
  0.1932062445_1698342642_6004297272_4878262694_0319954218_2378803210_3811145​90
  6_7729280350_9838344592_7210714495_4729261041_3378807649_9598674160_7827697​59
  4_1784866336_6792653022_6594598690_5177697043_1017564226_1489350712_9934497​21
  3_9594793993_5262359569_8250260525_5660501538_7635587817_8709159148_6787800​01
  8_9047375095_3646668376_0159595623_8758721064_2807064917_2318193821_5102971​00
  5_5085983115_6245282239_5693603230_4126121848_3058777289_5993452272_5154879​23
  5_0176948667_6196507796_7975788803_1141321162_8373996275_7293290870_9161149​69
  1_0433795838_7691660545_3675471594_2096004090_9235269470_0386425237_6152124​29
  1_9559601207_1199474637_4682120881_2503224600_2360167383_8202940058_4714355​92
  3_7008380850_7622281630_6532955554_5622541872_1182998216_8729690475_3754741​68
  4_8107119024_1876451777_0338712480_7685310255_1784413081_2009636745_5481002​35
  9_6163710640_0273901319_4779319675_6521022660_1014063765_6140459853_2032430​06
  7_7311393656_3570704001_7309147447_6651263962_0668950160_9685148444_5001971​24
  2_0452050499_8907437001_4649119078_6252980720_7231657066_3391430623_7802965​72
  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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