Average Error: 0.1 → 0.1
Time: 15.6s
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 r42369 = x;
        double r42370 = r42369 * r42369;
        double r42371 = 3.0;
        double r42372 = r42370 - r42371;
        double r42373 = 6.0;
        double r42374 = r42372 / r42373;
        return r42374;
}
↓
double f(double x) {
        double r42375 = x;
        double r42376 = 6.0;
        double r42377 = r42375 / r42376;
        double r42378 = r42377 * r42375;
        double r42379 = 3.0;
        double r42380 = r42379 / r42376;
        double r42381 = r42378 - r42380;
        return r42381;
}

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 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))