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THE FEUTEX TOOLKIT

Halley Root-Finding Step

Calculate a cubic-convergence root update using a function and its first two derivatives.

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01 Your input
02 Your result
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FormulaNext X = x-2*fx*df/(2*df**2-fx*ddf); Step = -2*fx*df/(2*df**2-fx*ddf)
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  • Calculate a cubic-convergence root update using a function and its first two derivatives.
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Worked example

Inputs

Current x
1.5 number
Function value
0.25 number
First derivative
3 number
Second derivative
2 number

Expected results

Next X
1.414285714 number
Step
-0.08571428571 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter current x, function value, first derivative, second derivative.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "x": 1.5,
  "fx": 0.25,
  "df": 3,
  "ddf": 2
}

Accuracy and scope

One update only. Derivatives must be evaluated at the supplied x; no global convergence guarantee.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.