Casio FX-115MS bug
11-08-2018, 04:17 PM (This post was last modified: 09-02-2019 07:45 PM by Albert Chan.)
Post: #11
 Albert Chan Senior Member Posts: 2,616 Joined: Jul 2018
RE: Casio FX-115MS bug
(11-07-2018 08:15 PM)Albert Chan Wrote:  The equation were *already* a depressed cubic, with r = 1/3, s = -1000100/2 ...
Do this another way, with X = u - r/u, where u³ = -(s + sign(s) √(s² + r³))
With r this small, and s negative, u³ ~ -2s = 1000100

u ~ 100.0033332
X = u - r/u = 100

I think I figured out the reason for loss of precision.
Instead of using above formula, it uses this:

X³ + (3r)X + (2s) = 0

X = ³√(-s + √(s² + r³)) + ³√(-s - √(s² + r³))

Above example, subtraction cancellation dropped the last term, we get X ~ u + 0 = u

Comment on previous posts:

Post #9: Y = X-100 had no effect, because Cubic Solver revert it back to depressed cubic.

Post #10: root reciprocal suffer less rounding errors because dropped term are smaller.
x = 0.00036663 (shift to depress cubic) + 0.9999666689 + 0.0000001344 (dropped) = 1.000333299
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 Messages In This Thread Casio FX-115MS bug - Albert Chan - 10-31-2018, 07:02 PM RE: Casio FX-115MS bug - klesl - 11-01-2018, 11:14 AM RE: Casio FX-115MS bug - ijabbott - 11-01-2018, 08:16 PM RE: Casio FX-115MS bug - G. Cook - 11-02-2018, 09:14 PM RE: Casio FX-115MS bug - Albert Chan - 11-03-2018, 02:41 PM RE: Casio FX-115MS bug - Albert Chan - 11-05-2018, 08:58 PM RE: Casio FX-115MS bug - Albert Chan - 11-07-2018, 08:15 PM RE: Casio FX-115MS bug - Albert Chan - 11-07-2018, 10:47 PM RE: Casio FX-115MS bug - Albert Chan - 11-08-2018 04:17 PM RE: Casio FX-115MS bug - Albert Chan - 11-24-2018, 07:25 PM RE: Casio FX-115MS bug - ijabbott - 11-24-2018, 08:28 PM RE: Casio FX-115MS bug - klesl - 11-07-2018, 08:33 PM RE: Casio FX-115MS bug - Albert Chan - 11-08-2018, 02:51 PM RE: Casio FX-115MS bug - brickviking - 11-28-2018, 01:01 AM

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