Average Error: 0.2 → 0.1
Time: 1.2s
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 r66453 = x;
        double r66454 = r66453 * r66453;
        double r66455 = 3.0;
        double r66456 = r66454 - r66455;
        double r66457 = 6.0;
        double r66458 = r66456 / r66457;
        return r66458;
}
↓
double f(double x) {
        double r66459 = x;
        double r66460 = 6.0;
        double r66461 = r66459 / r66460;
        double r66462 = r66459 * r66461;
        double r66463 = 3.0;
        double r66464 = r66463 / r66460;
        double r66465 = r66462 - r66464;
        return r66465;
}

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-sub0.2

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

  5. Applied *-un-lft-identity0.2

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

  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 2020060 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))