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 r88873 = x;
        double r88874 = r88873 * r88873;
        double r88875 = 3.0;
        double r88876 = r88874 - r88875;
        double r88877 = 6.0;
        double r88878 = r88876 / r88877;
        return r88878;
}
↓
double f(double x) {
        double r88879 = x;
        double r88880 = r88879 * r88879;
        double r88881 = 3.0;
        double r88882 = r88880 - r88881;
        double r88883 = 1.0;
        double r88884 = 6.0;
        double r88885 = r88883 / r88884;
        double r88886 = r88882 * r88885;
        return r88886;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))