Average Error: 4.9 → 0.1
Time: 8.9s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{x}{y}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} - 3
double f(double x, double y) {
        double r275121 = x;
        double r275122 = y;
        double r275123 = r275122 * r275122;
        double r275124 = r275121 / r275123;
        double r275125 = 3.0;
        double r275126 = r275124 - r275125;
        return r275126;
}
↓
double f(double x, double y) {
        double r275127 = x;
        double r275128 = y;
        double r275129 = r275127 / r275128;
        double r275130 = r275129 / r275128;
        double r275131 = 3.0;
        double r275132 = r275130 - r275131;
        return r275132;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 clear-num0.1

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

  6. Simplified0.1

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

  8. Applied associate-/r*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +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))