Average Error: 0.2 → 0.1
Time: 19.0s
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 r33636 = x;
        double r33637 = r33636 * r33636;
        double r33638 = 3.0;
        double r33639 = r33637 - r33638;
        double r33640 = 6.0;
        double r33641 = r33639 / r33640;
        return r33641;
}
↓
double f(double x) {
        double r33642 = x;
        double r33643 = 6.0;
        double r33644 = r33643 / r33642;
        double r33645 = r33642 / r33644;
        double r33646 = 3.0;
        double r33647 = r33646 / r33643;
        double r33648 = r33645 - r33647;
        return r33648;
}

Error

Bits error versus x

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Results

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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))