Average Error: 0.1 → 0.1
Time: 8.4s
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 r84415 = x;
        double r84416 = r84415 * r84415;
        double r84417 = 3.0;
        double r84418 = r84416 - r84417;
        double r84419 = 6.0;
        double r84420 = r84418 / r84419;
        return r84420;
}
↓
double f(double x) {
        double r84421 = x;
        double r84422 = 6.0;
        double r84423 = r84421 / r84422;
        double r84424 = r84421 * r84423;
        double r84425 = 3.0;
        double r84426 = r84425 / r84422;
        double r84427 = r84424 - r84426;
        return r84427;
}

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. 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 2020045 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))