Average Error: 0.1 → 0.1
Time: 8.0s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x}{6} - \frac{3}{6}
double f(double x) {
        double r123320 = x;
        double r123321 = r123320 * r123320;
        double r123322 = 3.0;
        double r123323 = r123321 - r123322;
        double r123324 = 6.0;
        double r123325 = r123323 / r123324;
        return r123325;
}
↓
double f(double x) {
        double r123326 = x;
        double r123327 = r123326 * r123326;
        double r123328 = 6.0;
        double r123329 = r123327 / r123328;
        double r123330 = 3.0;
        double r123331 = r123330 / r123328;
        double r123332 = r123329 - r123331;
        return r123332;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))