Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\frac{x \cdot x - 3.0}{6.0}\]
↓
\[\frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}\]
\frac{x \cdot x - 3.0}{6.0}
↓
\frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}
double f(double x) {
        double r3052810 = x;
        double r3052811 = r3052810 * r3052810;
        double r3052812 = 3.0;
        double r3052813 = r3052811 - r3052812;
        double r3052814 = 6.0;
        double r3052815 = r3052813 / r3052814;
        return r3052815;
}
↓
double f(double x) {
        double r3052816 = x;
        double r3052817 = 6.0;
        double r3052818 = r3052817 / r3052816;
        double r3052819 = r3052816 / r3052818;
        double r3052820 = 3.0;
        double r3052821 = r3052820 / r3052817;
        double r3052822 = r3052819 - r3052821;
        return r3052822;
}

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

    \[\frac{x \cdot x - 3.0}{6.0}\]
  2. Using strategy rm

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6.0} - \frac{3.0}{6.0}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{6.0}{x}}} - \frac{3.0}{6.0}\]

  6. Final simplification0.1

    \[\leadsto \frac{x}{\frac{6.0}{x}} - \frac{3.0}{6.0}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))