Average Error: 0.1 → 0.1
Time: 11.7s
Precision: 64
\[\frac{x \cdot x - 3.0}{6.0}\]
↓
\[\frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}\]
\frac{x \cdot x - 3.0}{6.0}
↓
\frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}
double f(double x) {
        double r5017484 = x;
        double r5017485 = r5017484 * r5017484;
        double r5017486 = 3.0;
        double r5017487 = r5017485 - r5017486;
        double r5017488 = 6.0;
        double r5017489 = r5017487 / r5017488;
        return r5017489;
}
↓
double f(double x) {
        double r5017490 = x;
        double r5017491 = 6.0;
        double r5017492 = r5017491 / r5017490;
        double r5017493 = r5017490 / r5017492;
        double r5017494 = 3.0;
        double r5017495 = r5017494 / r5017491;
        double r5017496 = r5017493 - r5017495;
        return r5017496;
}

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

    \[\frac{x \cdot x - 3.0}{6.0}\]
  2. Using strategy rm

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6.0} - \frac{3.0}{6.0}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{6.0}{x}}} - \frac{3.0}{6.0}\]

  6. Final simplification0.1

    \[\leadsto \frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))