Average Error: 0.1 → 0.1
Time: 15.8s
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 r71343 = x;
        double r71344 = r71343 * r71343;
        double r71345 = 3.0;
        double r71346 = r71344 - r71345;
        double r71347 = 6.0;
        double r71348 = r71346 / r71347;
        return r71348;
}
↓
double f(double x) {
        double r71349 = x;
        double r71350 = 6.0;
        double r71351 = r71349 / r71350;
        double r71352 = r71351 * r71349;
        double r71353 = 3.0;
        double r71354 = r71353 / r71350;
        double r71355 = r71352 - r71354;
        return r71355;
}

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 2019325 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))