Average Error: 0.1 → 0.1
Time: 16.1s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
double f(double x) {
        double r39551 = x;
        double r39552 = r39551 * r39551;
        double r39553 = 3.0;
        double r39554 = r39552 - r39553;
        double r39555 = 6.0;
        double r39556 = r39554 / r39555;
        return r39556;
}
↓
double f(double x) {
        double r39557 = x;
        double r39558 = 6.0;
        double r39559 = r39557 / r39558;
        double r39560 = r39557 * r39559;
        double r39561 = 3.0;
        double r39562 = r39561 / r39558;
        double r39563 = r39560 - r39562;
        return r39563;
}

Error

Bits error versus x

Try it out

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

    \[\leadsto \color{blue}{x \cdot \frac{x}{6}} - \frac{3}{6}\]

  5. Final simplification0.1

    \[\leadsto x \cdot \frac{x}{6} - \frac{3}{6}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))