Average Error: 0.1 → 0.2
Time: 7.3s
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 r92854 = x;
        double r92855 = r92854 * r92854;
        double r92856 = 3.0;
        double r92857 = r92855 - r92856;
        double r92858 = 6.0;
        double r92859 = r92857 / r92858;
        return r92859;
}
↓
double f(double x) {
        double r92860 = 1.0;
        double r92861 = 6.0;
        double r92862 = x;
        double r92863 = r92862 * r92862;
        double r92864 = 3.0;
        double r92865 = r92863 - r92864;
        double r92866 = r92860 / r92865;
        double r92867 = r92861 * r92866;
        double r92868 = r92860 / r92867;
        return r92868;
}

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