Average Error: 0.1 → 0.2
Time: 5.8s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{6 \cdot \frac{1}{x \cdot x - 3}}
double f(double x) {
        double r96890 = x;
        double r96891 = r96890 * r96890;
        double r96892 = 3.0;
        double r96893 = r96891 - r96892;
        double r96894 = 6.0;
        double r96895 = r96893 / r96894;
        return r96895;
}
↓
double f(double x) {
        double r96896 = 1.0;
        double r96897 = 6.0;
        double r96898 = x;
        double r96899 = r96898 * r96898;
        double r96900 = 3.0;
        double r96901 = r96899 - r96900;
        double r96902 = r96896 / r96901;
        double r96903 = r96897 * r96902;
        double r96904 = r96896 / r96903;
        return r96904;
}

Error

Bits error versus x

Try it out

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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{6}{x \cdot x - 3}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))