Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{6} \cdot x - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{6} \cdot x - \frac{3}{6}
double f(double x) {
        double r50908 = x;
        double r50909 = r50908 * r50908;
        double r50910 = 3.0;
        double r50911 = r50909 - r50910;
        double r50912 = 6.0;
        double r50913 = r50911 / r50912;
        return r50913;
}
↓
double f(double x) {
        double r50914 = x;
        double r50915 = 6.0;
        double r50916 = r50914 / r50915;
        double r50917 = r50916 * r50914;
        double r50918 = 3.0;
        double r50919 = r50918 / r50915;
        double r50920 = r50917 - r50919;
        return r50920;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{\frac{x}{6} \cdot x} - \frac{3}{6}\]

  5. Final simplification0.1

    \[\leadsto \frac{x}{6} \cdot x - \frac{3}{6}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))