Casio FX-115MS bug

[Albert Chan]

(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