Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\frac{x \cdot x - 3.0}{6.0}\]
↓
\[x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]
\frac{x \cdot x - 3.0}{6.0}
↓
x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}
double f(double x) {
        double r2085742 = x;
        double r2085743 = r2085742 * r2085742;
        double r2085744 = 3.0;
        double r2085745 = r2085743 - r2085744;
        double r2085746 = 6.0;
        double r2085747 = r2085745 / r2085746;
        return r2085747;
}
↓
double f(double x) {
        double r2085748 = x;
        double r2085749 = 6.0;
        double r2085750 = r2085748 / r2085749;
        double r2085751 = r2085748 * r2085750;
        double r2085752 = 3.0;
        double r2085753 = r2085752 / r2085749;
        double r2085754 = r2085751 - r2085753;
        return r2085754;
}

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

    \[\frac{x \cdot x - 3.0}{6.0}\]
  2. Using strategy rm

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6.0} - \frac{3.0}{6.0}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x \cdot x}{\color{blue}{1 \cdot 6.0}} - \frac{3.0}{6.0}\]

  6. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{x}{6.0}} - \frac{3.0}{6.0}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{x} \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]

  8. Final simplification0.1

    \[\leadsto x \cdot \frac{x}{6.0} - \frac{3.0}{6.0}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))