Average Error: 4.9 → 0.1
Time: 8.6s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{\sqrt{1}}{\sqrt{1}}}{y \cdot \frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{\sqrt{1}}{\sqrt{1}}}{y \cdot \frac{y}{x}} - 3
double f(double x, double y) {
        double r242545 = x;
        double r242546 = y;
        double r242547 = r242546 * r242546;
        double r242548 = r242545 / r242547;
        double r242549 = 3.0;
        double r242550 = r242548 - r242549;
        return r242550;
}
↓
double f(double x, double y) {
        double r242551 = 1.0;
        double r242552 = sqrt(r242551);
        double r242553 = r242552 / r242552;
        double r242554 = y;
        double r242555 = x;
        double r242556 = r242554 / r242555;
        double r242557 = r242554 * r242556;
        double r242558 = r242553 / r242557;
        double r242559 = 3.0;
        double r242560 = r242558 - r242559;
        return r242560;
}

Error

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Results

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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 *-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 add-sqr-sqrt0.1

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

  11. Applied add-sqr-sqrt0.1

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

  12. Applied times-frac0.1

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

  13. Applied associate-/l*0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

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))