Average Error: 0.2 → 0.2
Time: 9.4s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x - 3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x - 3}{6}
double f(double x) {
        double r56121 = x;
        double r56122 = r56121 * r56121;
        double r56123 = 3.0;
        double r56124 = r56122 - r56123;
        double r56125 = 6.0;
        double r56126 = r56124 / r56125;
        return r56126;
}
↓
double f(double x) {
        double r56127 = x;
        double r56128 = r56127 * r56127;
        double r56129 = 3.0;
        double r56130 = r56128 - r56129;
        double r56131 = 6.0;
        double r56132 = r56130 / r56131;
        return r56132;
}

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 *-un-lft-identity0.2

    \[\leadsto \frac{x \cdot x - 3}{\color{blue}{1 \cdot 6}}\]

  4. Applied add-sqr-sqrt0.8

    \[\leadsto \frac{x \cdot x - \color{blue}{\sqrt{3} \cdot \sqrt{3}}}{1 \cdot 6}\]

  5. Applied difference-of-squares0.8

    \[\leadsto \frac{\color{blue}{\left(x + \sqrt{3}\right) \cdot \left(x - \sqrt{3}\right)}}{1 \cdot 6}\]

  6. Applied times-frac0.7

    \[\leadsto \color{blue}{\frac{x + \sqrt{3}}{1} \cdot \frac{x - \sqrt{3}}{6}}\]

  7. Simplified0.7

    \[\leadsto \color{blue}{\left(x + \sqrt{3}\right)} \cdot \frac{x - \sqrt{3}}{6}\]
  8. Using strategy rm

  9. Applied associate-*r/0.8

    \[\leadsto \color{blue}{\frac{\left(x + \sqrt{3}\right) \cdot \left(x - \sqrt{3}\right)}{6}}\]

  10. Simplified0.2

    \[\leadsto \frac{\color{blue}{x \cdot x - 3}}{6}\]

  11. Final simplification0.2

    \[\leadsto \frac{x \cdot x - 3}{6}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))