Average Error: 0.1 → 0.1
Time: 1.3s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{\frac{6}{x}} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{\frac{6}{x}} - \frac{3}{6}
double f(double x) {
        double r53815 = x;
        double r53816 = r53815 * r53815;
        double r53817 = 3.0;
        double r53818 = r53816 - r53817;
        double r53819 = 6.0;
        double r53820 = r53818 / r53819;
        return r53820;
}
↓
double f(double x) {
        double r53821 = x;
        double r53822 = 6.0;
        double r53823 = r53822 / r53821;
        double r53824 = r53821 / r53823;
        double r53825 = 3.0;
        double r53826 = r53825 / r53822;
        double r53827 = r53824 - r53826;
        return r53827;
}

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. Using strategy rm

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))