Average Error: 0.2 → 0.1
Time: 1.2s
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 r81071 = x;
        double r81072 = r81071 * r81071;
        double r81073 = 3.0;
        double r81074 = r81072 - r81073;
        double r81075 = 6.0;
        double r81076 = r81074 / r81075;
        return r81076;
}
↓
double f(double x) {
        double r81077 = x;
        double r81078 = 6.0;
        double r81079 = r81078 / r81077;
        double r81080 = r81077 / r81079;
        double r81081 = 3.0;
        double r81082 = r81081 / r81078;
        double r81083 = r81080 - r81082;
        return r81083;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  3. Applied div-sub0.2

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]
  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 2019352 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))