Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\frac{x \cdot x - 3.0}{6.0}\]
↓
\[x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]
\frac{x \cdot x - 3.0}{6.0}
↓
x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}
double f(double x) {
        double r1109304 = x;
        double r1109305 = r1109304 * r1109304;
        double r1109306 = 3.0;
        double r1109307 = r1109305 - r1109306;
        double r1109308 = 6.0;
        double r1109309 = r1109307 / r1109308;
        return r1109309;
}
↓
double f(double x) {
        double r1109310 = x;
        double r1109311 = 6.0;
        double r1109312 = r1109310 / r1109311;
        double r1109313 = r1109310 * r1109312;
        double r1109314 = 3.0;
        double r1109315 = r1109314 / r1109311;
        double r1109316 = r1109313 - r1109315;
        return r1109316;
}

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 *-un-lft-identity0.1

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6.0}} - \frac{3.0}{6.0}\]

  6. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6.0}} - \frac{3.0}{6.0}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))