Average Error: 0.2 → 0.1
Time: 19.6s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{\frac{6}{x}} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{\frac{6}{x}} - \frac{3}{6}
double f(double x) {
        double r53875 = x;
        double r53876 = r53875 * r53875;
        double r53877 = 3.0;
        double r53878 = r53876 - r53877;
        double r53879 = 6.0;
        double r53880 = r53878 / r53879;
        return r53880;
}
↓
double f(double x) {
        double r53881 = x;
        double r53882 = 6.0;
        double r53883 = r53882 / r53881;
        double r53884 = r53881 / r53883;
        double r53885 = 3.0;
        double r53886 = r53885 / r53882;
        double r53887 = r53884 - r53886;
        return r53887;
}

Error

Bits error versus x

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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-sub0.1

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

  4. Simplified0.1

    \[\leadsto \color{blue}{\frac{x}{6} \cdot x} - \frac{3}{6}\]
  5. Using strategy rm

  6. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6}} - \frac{3}{6}\]
  7. Using strategy rm

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))