Average Error: 0.1 → 0.1
Time: 7.6s
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 r62979 = x;
        double r62980 = r62979 * r62979;
        double r62981 = 3.0;
        double r62982 = r62980 - r62981;
        double r62983 = 6.0;
        double r62984 = r62982 / r62983;
        return r62984;
}
↓
double f(double x) {
        double r62985 = x;
        double r62986 = 6.0;
        double r62987 = r62986 / r62985;
        double r62988 = r62985 / r62987;
        double r62989 = 3.0;
        double r62990 = r62989 / r62986;
        double r62991 = r62988 - r62990;
        return r62991;
}

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

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

  3. Applied div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]
  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 2019212 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))