Average Error: 0.1 → 0.1
Time: 11.5s
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 r5029361 = x;
        double r5029362 = r5029361 * r5029361;
        double r5029363 = 3.0;
        double r5029364 = r5029362 - r5029363;
        double r5029365 = 6.0;
        double r5029366 = r5029364 / r5029365;
        return r5029366;
}
↓
double f(double x) {
        double r5029367 = x;
        double r5029368 = 6.0;
        double r5029369 = r5029368 / r5029367;
        double r5029370 = r5029367 / r5029369;
        double r5029371 = 3.0;
        double r5029372 = r5029371 / r5029368;
        double r5029373 = r5029370 - r5029372;
        return r5029373;
}

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

    \[\frac{x \cdot x - 3.0}{6.0}\]
  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))