Average Error: 5.3 → 0.1
Time: 2.0s
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 r310473 = x;
        double r310474 = y;
        double r310475 = r310474 * r310474;
        double r310476 = r310473 / r310475;
        double r310477 = 3.0;
        double r310478 = r310476 - r310477;
        return r310478;
}
↓
double f(double x, double y) {
        double r310479 = 1.0;
        double r310480 = y;
        double r310481 = x;
        double r310482 = r310480 / r310481;
        double r310483 = r310480 * r310482;
        double r310484 = r310479 / r310483;
        double r310485 = 3.0;
        double r310486 = r310484 - r310485;
        return r310486;
}

Error

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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-sqrt32.0

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

  8. Applied *-un-lft-identity32.0

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

  9. Applied times-frac32.0

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

  10. Applied add-sqr-sqrt32.1

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

  11. Applied times-frac32.1

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

  12. Simplified32.0

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

  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 2020039 
(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))