Average Error: 0.2 → 0.2
Time: 1.2s
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 r46864 = x;
        double r46865 = r46864 * r46864;
        double r46866 = 3.0;
        double r46867 = r46865 - r46866;
        double r46868 = 6.0;
        double r46869 = r46867 / r46868;
        return r46869;
}
↓
double f(double x) {
        double r46870 = x;
        double r46871 = r46870 * r46870;
        double r46872 = 6.0;
        double r46873 = r46871 / r46872;
        double r46874 = 3.0;
        double r46875 = r46874 / r46872;
        double r46876 = r46873 - r46875;
        return r46876;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))