Average Error: 0.1 → 0.1
Time: 7.9s
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 r55153 = x;
        double r55154 = r55153 * r55153;
        double r55155 = 3.0;
        double r55156 = r55154 - r55155;
        double r55157 = 6.0;
        double r55158 = r55156 / r55157;
        return r55158;
}
↓
double f(double x) {
        double r55159 = x;
        double r55160 = 6.0;
        double r55161 = r55160 / r55159;
        double r55162 = r55159 / r55161;
        double r55163 = 3.0;
        double r55164 = r55163 / r55160;
        double r55165 = r55162 - r55164;
        return r55165;
}

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 2019212 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))