Average Error: 5.1 → 0.1
Time: 2.5s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{\frac{y}{x}}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{\frac{y}{x}}}{y} - 3
double f(double x, double y) {
        double r237794 = x;
        double r237795 = y;
        double r237796 = r237795 * r237795;
        double r237797 = r237794 / r237796;
        double r237798 = 3.0;
        double r237799 = r237797 - r237798;
        return r237799;
}
↓
double f(double x, double y) {
        double r237800 = 1.0;
        double r237801 = y;
        double r237802 = x;
        double r237803 = r237801 / r237802;
        double r237804 = r237800 / r237803;
        double r237805 = r237804 / r237801;
        double r237806 = 3.0;
        double r237807 = r237805 - r237806;
        return r237807;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.1
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.1

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

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{y}{\frac{x}{y}}}} - 3\]
  9. Using strategy rm

  10. Applied associate-/r/0.1

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

  11. Applied associate-/r*0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{y}{x}}}{y} - 3\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3)

  (- (/ x (* y y)) 3))