Average Error: 0.2 → 0.1
Time: 17.4s
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 r49710 = x;
        double r49711 = r49710 * r49710;
        double r49712 = 3.0;
        double r49713 = r49711 - r49712;
        double r49714 = 6.0;
        double r49715 = r49713 / r49714;
        return r49715;
}
↓
double f(double x) {
        double r49716 = x;
        double r49717 = 6.0;
        double r49718 = r49716 / r49717;
        double r49719 = r49718 * r49716;
        double r49720 = 3.0;
        double r49721 = r49720 / r49717;
        double r49722 = r49719 - r49721;
        return r49722;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  3. Applied div-sub0.2

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

  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 2019347 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))