Average Error: 0.1 → 0.1
Time: 18.0s
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 r59135 = x;
        double r59136 = r59135 * r59135;
        double r59137 = 3.0;
        double r59138 = r59136 - r59137;
        double r59139 = 6.0;
        double r59140 = r59138 / r59139;
        return r59140;
}
↓
double f(double x) {
        double r59141 = x;
        double r59142 = 6.0;
        double r59143 = r59141 / r59142;
        double r59144 = r59143 * r59141;
        double r59145 = 3.0;
        double r59146 = r59145 / r59142;
        double r59147 = r59144 - r59146;
        return r59147;
}

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 2019326 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))