Average Error: 0.2 → 0.2
Time: 2.5s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\left(x \cdot x - 3\right) \cdot \frac{1}{6}\]
\frac{x \cdot x - 3}{6}
↓
\left(x \cdot x - 3\right) \cdot \frac{1}{6}
double f(double x) {
        double r122871 = x;
        double r122872 = r122871 * r122871;
        double r122873 = 3.0;
        double r122874 = r122872 - r122873;
        double r122875 = 6.0;
        double r122876 = r122874 / r122875;
        return r122876;
}
↓
double f(double x) {
        double r122877 = x;
        double r122878 = r122877 * r122877;
        double r122879 = 3.0;
        double r122880 = r122878 - r122879;
        double r122881 = 1.0;
        double r122882 = 6.0;
        double r122883 = r122881 / r122882;
        double r122884 = r122880 * r122883;
        return r122884;
}

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-inv0.2

    \[\leadsto \color{blue}{\left(x \cdot x - 3\right) \cdot \frac{1}{6}}\]

  4. Final simplification0.2

    \[\leadsto \left(x \cdot x - 3\right) \cdot \frac{1}{6}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))