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 r59601 = x;
        double r59602 = r59601 * r59601;
        double r59603 = 3.0;
        double r59604 = r59602 - r59603;
        double r59605 = 6.0;
        double r59606 = r59604 / r59605;
        return r59606;
}
↓
double f(double x) {
        double r59607 = x;
        double r59608 = 6.0;
        double r59609 = r59608 / r59607;
        double r59610 = r59607 / r59609;
        double r59611 = 3.0;
        double r59612 = r59611 / r59608;
        double r59613 = r59610 - r59612;
        return r59613;
}

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 2019198 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))