Average Error: 0.2 → 0.2
Time: 2.3s
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 r74802 = x;
        double r74803 = r74802 * r74802;
        double r74804 = 3.0;
        double r74805 = r74803 - r74804;
        double r74806 = 6.0;
        double r74807 = r74805 / r74806;
        return r74807;
}
↓
double f(double x) {
        double r74808 = x;
        double r74809 = r74808 * r74808;
        double r74810 = 3.0;
        double r74811 = r74809 - r74810;
        double r74812 = 1.0;
        double r74813 = 6.0;
        double r74814 = r74812 / r74813;
        double r74815 = r74811 * r74814;
        return r74815;
}

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