Casio FX-115MS bug

[Albert Chan]

Hi, klesl

I don't expect exact result. But the result seems not due to rounding errors.
Relative errors of 0.003% is not the upper bound. Try this:

X³ + 11 X - 1000100 = 0

Cubic Solver still returned real root of 100.0033332

For above cubic, u is still about 100.0033332, but r is now 11/3

X = u - r/u = 99.96666778, so Solver result only have 3 good digits.

If it is a generalized solver, maybe 3 or 4 good digits is enough.
But, this is a specialized Cubic Solver, with known formula for it.

Even worse case may be possible (example, by adding X² term)

Update: Let Y = X - 100, hoping for better luck:

Y³ + 300 Y² + 30011 Y + 1000 = 0

Expecting Y correction of -0.03333222. Instead, I got +0.003333223
Cubic Solver get the sign wrong ! (Relative error of 110% !)