Average Error: 0.1 → 0.1
Time: 2.3s
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 r99637 = x;
        double r99638 = r99637 * r99637;
        double r99639 = 3.0;
        double r99640 = r99638 - r99639;
        double r99641 = 6.0;
        double r99642 = r99640 / r99641;
        return r99642;
}
↓
double f(double x) {
        double r99643 = x;
        double r99644 = r99643 * r99643;
        double r99645 = 6.0;
        double r99646 = r99644 / r99645;
        double r99647 = 3.0;
        double r99648 = r99647 / r99645;
        double r99649 = r99646 - r99648;
        return r99649;
}

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 2019346 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))