Average Error: 0.1 → 0.1
Time: 16.2s
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 r61752 = x;
        double r61753 = r61752 * r61752;
        double r61754 = 3.0;
        double r61755 = r61753 - r61754;
        double r61756 = 6.0;
        double r61757 = r61755 / r61756;
        return r61757;
}
↓
double f(double x) {
        double r61758 = x;
        double r61759 = 6.0;
        double r61760 = r61758 / r61759;
        double r61761 = r61760 * r61758;
        double r61762 = 3.0;
        double r61763 = r61762 / r61759;
        double r61764 = r61761 - r61763;
        return r61764;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot x - 3}{6}\]
  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 2019325 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))