Average Error: 0.1 → 0.1
Time: 17.8s
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 r74669 = x;
        double r74670 = r74669 * r74669;
        double r74671 = 3.0;
        double r74672 = r74670 - r74671;
        double r74673 = 6.0;
        double r74674 = r74672 / r74673;
        return r74674;
}
↓
double f(double x) {
        double r74675 = x;
        double r74676 = 6.0;
        double r74677 = r74675 / r74676;
        double r74678 = r74677 * r74675;
        double r74679 = 3.0;
        double r74680 = r74679 / r74676;
        double r74681 = r74678 - r74680;
        return r74681;
}

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))