Average Error: 0.2 → 0.1
Time: 1.2s
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 r53255 = x;
        double r53256 = r53255 * r53255;
        double r53257 = 3.0;
        double r53258 = r53256 - r53257;
        double r53259 = 6.0;
        double r53260 = r53258 / r53259;
        return r53260;
}
↓
double f(double x) {
        double r53261 = x;
        double r53262 = 6.0;
        double r53263 = r53262 / r53261;
        double r53264 = r53261 / r53263;
        double r53265 = 3.0;
        double r53266 = r53265 / r53262;
        double r53267 = r53264 - r53266;
        return r53267;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied div-sub0.2

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]
  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 2019352 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))