Average Error: 5.0 → 0.1
Time: 18.4s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y \cdot \frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y \cdot \frac{y}{x}} - 3
double f(double x, double y) {
        double r356964 = x;
        double r356965 = y;
        double r356966 = r356965 * r356965;
        double r356967 = r356964 / r356966;
        double r356968 = 3.0;
        double r356969 = r356967 - r356968;
        return r356969;
}
↓
double f(double x, double y) {
        double r356970 = 1.0;
        double r356971 = y;
        double r356972 = x;
        double r356973 = r356971 / r356972;
        double r356974 = r356971 * r356973;
        double r356975 = r356970 / r356974;
        double r356976 = 3.0;
        double r356977 = r356975 - r356976;
        return r356977;
}

Error

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

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

  7. Applied add-sqr-sqrt32.2

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

  8. Applied *-un-lft-identity32.2

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

  9. Applied times-frac32.2

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

  10. Applied add-sqr-sqrt32.3

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

  11. Applied times-frac32.3

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

  12. Simplified32.2

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +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))