Average Error: 0.1 → 0.1
Time: 16.6s
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 r48871 = x;
        double r48872 = r48871 * r48871;
        double r48873 = 3.0;
        double r48874 = r48872 - r48873;
        double r48875 = 6.0;
        double r48876 = r48874 / r48875;
        return r48876;
}
↓
double f(double x) {
        double r48877 = x;
        double r48878 = 6.0;
        double r48879 = r48877 / r48878;
        double r48880 = r48879 * r48877;
        double r48881 = 3.0;
        double r48882 = r48881 / r48878;
        double r48883 = r48880 - r48882;
        return r48883;
}

Error

Bits error versus x

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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 2019304 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))