Average Error: 5.4 → 0.1
Time: 3.8s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{\frac{x}{y}}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{\frac{x}{y}}} - 3
double f(double x, double y) {
        double r283840 = x;
        double r283841 = y;
        double r283842 = r283841 * r283841;
        double r283843 = r283840 / r283842;
        double r283844 = 3.0;
        double r283845 = r283843 - r283844;
        return r283845;
}
↓
double f(double x, double y) {
        double r283846 = 1.0;
        double r283847 = y;
        double r283848 = x;
        double r283849 = r283848 / r283847;
        double r283850 = r283847 / r283849;
        double r283851 = r283846 / r283850;
        double r283852 = 3.0;
        double r283853 = r283851 - r283852;
        return r283853;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +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))