Average Error: 0.1 → 0.1
Time: 17.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{6} \cdot x - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{6} \cdot x - \frac{3}{6}
double f(double x) {
        double r66292 = x;
        double r66293 = r66292 * r66292;
        double r66294 = 3.0;
        double r66295 = r66293 - r66294;
        double r66296 = 6.0;
        double r66297 = r66295 / r66296;
        return r66297;
}
↓
double f(double x) {
        double r66298 = x;
        double r66299 = 6.0;
        double r66300 = r66298 / r66299;
        double r66301 = r66300 * r66298;
        double r66302 = 3.0;
        double r66303 = r66302 / r66299;
        double r66304 = r66301 - r66303;
        return r66304;
}

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 div-sub0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))