Average Error: 5.0 → 0.1
Time: 22.1s
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 r219448 = x;
        double r219449 = y;
        double r219450 = r219449 * r219449;
        double r219451 = r219448 / r219450;
        double r219452 = 3.0;
        double r219453 = r219451 - r219452;
        return r219453;
}
↓
double f(double x, double y) {
        double r219454 = 1.0;
        double r219455 = y;
        double r219456 = x;
        double r219457 = r219455 / r219456;
        double r219458 = r219455 * r219457;
        double r219459 = r219454 / r219458;
        double r219460 = 3.0;
        double r219461 = r219459 - r219460;
        return r219461;
}

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 *-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. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(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))