Average Error: 0.2 → 0.1
Time: 17.6s
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 r57954 = x;
        double r57955 = r57954 * r57954;
        double r57956 = 3.0;
        double r57957 = r57955 - r57956;
        double r57958 = 6.0;
        double r57959 = r57957 / r57958;
        return r57959;
}
↓
double f(double x) {
        double r57960 = x;
        double r57961 = 6.0;
        double r57962 = r57960 / r57961;
        double r57963 = r57962 * r57960;
        double r57964 = 3.0;
        double r57965 = r57964 / r57961;
        double r57966 = r57963 - r57965;
        return r57966;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x \cdot x - 3}{6}\]
  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 2019306 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))