Average Error: 0.1 → 0.1
Time: 15.7s
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 r63560 = x;
        double r63561 = r63560 * r63560;
        double r63562 = 3.0;
        double r63563 = r63561 - r63562;
        double r63564 = 6.0;
        double r63565 = r63563 / r63564;
        return r63565;
}
↓
double f(double x) {
        double r63566 = x;
        double r63567 = 6.0;
        double r63568 = r63566 / r63567;
        double r63569 = r63568 * r63566;
        double r63570 = 3.0;
        double r63571 = r63570 / r63567;
        double r63572 = r63569 - r63571;
        return r63572;
}

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