Average Error: 0.1 → 0.1
Time: 7.7s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
double f(double x) {
        double r52213 = x;
        double r52214 = r52213 * r52213;
        double r52215 = 3.0;
        double r52216 = r52214 - r52215;
        double r52217 = 6.0;
        double r52218 = r52216 / r52217;
        return r52218;
}
↓
double f(double x) {
        double r52219 = x;
        double r52220 = 6.0;
        double r52221 = r52219 / r52220;
        double r52222 = r52219 * r52221;
        double r52223 = 3.0;
        double r52224 = r52223 / r52220;
        double r52225 = r52222 - r52224;
        return r52225;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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. Using strategy rm

  5. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6}} - \frac{3}{6}\]

  6. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6}} - \frac{3}{6}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))