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 r50823 = x;
        double r50824 = r50823 * r50823;
        double r50825 = 3.0;
        double r50826 = r50824 - r50825;
        double r50827 = 6.0;
        double r50828 = r50826 / r50827;
        return r50828;
}
↓
double f(double x) {
        double r50829 = x;
        double r50830 = 6.0;
        double r50831 = r50829 / r50830;
        double r50832 = r50831 * r50829;
        double r50833 = 3.0;
        double r50834 = r50833 / r50830;
        double r50835 = r50832 - r50834;
        return r50835;
}

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 2019304 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))