Average Error: 0.2 → 0.1
Time: 16.6s
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 r108746 = x;
        double r108747 = r108746 * r108746;
        double r108748 = 3.0;
        double r108749 = r108747 - r108748;
        double r108750 = 6.0;
        double r108751 = r108749 / r108750;
        return r108751;
}
↓
double f(double x) {
        double r108752 = x;
        double r108753 = 6.0;
        double r108754 = r108752 / r108753;
        double r108755 = r108754 * r108752;
        double r108756 = 3.0;
        double r108757 = r108756 / r108753;
        double r108758 = r108755 - r108757;
        return r108758;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))