Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
double f(double x) {
        double r53487 = x;
        double r53488 = r53487 * r53487;
        double r53489 = 3.0;
        double r53490 = r53488 - r53489;
        double r53491 = 6.0;
        double r53492 = r53490 / r53491;
        return r53492;
}
↓
double f(double x) {
        double r53493 = x;
        double r53494 = 6.0;
        double r53495 = r53493 / r53494;
        double r53496 = r53493 * r53495;
        double r53497 = 3.0;
        double r53498 = r53497 / r53494;
        double r53499 = r53496 - r53498;
        return r53499;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))