Average Error: 0.1 → 0.1
Time: 1.4s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x}{6} - \frac{3}{6}
double f(double x) {
        double r49888 = x;
        double r49889 = r49888 * r49888;
        double r49890 = 3.0;
        double r49891 = r49889 - r49890;
        double r49892 = 6.0;
        double r49893 = r49891 / r49892;
        return r49893;
}
↓
double f(double x) {
        double r49894 = x;
        double r49895 = r49894 * r49894;
        double r49896 = 6.0;
        double r49897 = r49895 / r49896;
        double r49898 = 3.0;
        double r49899 = r49898 / r49896;
        double r49900 = r49897 - r49899;
        return r49900;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))