Average Error: 4.5 → 0.1
Time: 13.3s
Precision: 64
\[\frac{x}{y \cdot y} - 3.0\]
↓
\[\frac{\frac{1}{\frac{y}{x}}}{y} - 3.0\]
\frac{x}{y \cdot y} - 3.0
↓
\frac{\frac{1}{\frac{y}{x}}}{y} - 3.0
double f(double x, double y) {
        double r10604081 = x;
        double r10604082 = y;
        double r10604083 = r10604082 * r10604082;
        double r10604084 = r10604081 / r10604083;
        double r10604085 = 3.0;
        double r10604086 = r10604084 - r10604085;
        return r10604086;
}
↓
double f(double x, double y) {
        double r10604087 = 1.0;
        double r10604088 = y;
        double r10604089 = x;
        double r10604090 = r10604088 / r10604089;
        double r10604091 = r10604087 / r10604090;
        double r10604092 = r10604091 / r10604088;
        double r10604093 = 3.0;
        double r10604094 = r10604092 - r10604093;
        return r10604094;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.5
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3.0\]

Derivation

  1. Initial program 4.5

    \[\frac{x}{y \cdot y} - 3.0\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3.0\]
  4. Using strategy rm

  5. Applied clear-num0.1

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3.0\]
  6. Using strategy rm

  7. Applied associate-/r/0.1

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot y}} - 3.0\]

  8. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{y}} - 3.0\]

  9. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{y}{x}}}{y} - 3.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))