Average Error: 0.1 → 0.1
Time: 7.2s
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 r59271 = x;
        double r59272 = r59271 * r59271;
        double r59273 = 3.0;
        double r59274 = r59272 - r59273;
        double r59275 = 6.0;
        double r59276 = r59274 / r59275;
        return r59276;
}
↓
double f(double x) {
        double r59277 = x;
        double r59278 = 6.0;
        double r59279 = r59278 / r59277;
        double r59280 = r59277 / r59279;
        double r59281 = 3.0;
        double r59282 = r59281 / r59278;
        double r59283 = r59280 - r59282;
        return r59283;
}

Error

Bits error versus x

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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 2019195 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))