Average Error: 0.2 → 0.2
Time: 2.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{\frac{6}{x \cdot x - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{\frac{6}{x \cdot x - 3}}
double f(double x) {
        double r57682 = x;
        double r57683 = r57682 * r57682;
        double r57684 = 3.0;
        double r57685 = r57683 - r57684;
        double r57686 = 6.0;
        double r57687 = r57685 / r57686;
        return r57687;
}
↓
double f(double x) {
        double r57688 = 1.0;
        double r57689 = 6.0;
        double r57690 = x;
        double r57691 = r57690 * r57690;
        double r57692 = 3.0;
        double r57693 = r57691 - r57692;
        double r57694 = r57689 / r57693;
        double r57695 = r57688 / r57694;
        return r57695;
}

Error

Bits error versus x

Try it out

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 clear-num0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))