Average Error: 5.3 → 0.1
Time: 8.5s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{x}{y}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} - 3
double f(double x, double y) {
        double r358116 = x;
        double r358117 = y;
        double r358118 = r358117 * r358117;
        double r358119 = r358116 / r358118;
        double r358120 = 3.0;
        double r358121 = r358119 - r358120;
        return r358121;
}
↓
double f(double x, double y) {
        double r358122 = x;
        double r358123 = y;
        double r358124 = r358122 / r358123;
        double r358125 = r358124 / r358123;
        double r358126 = 3.0;
        double r358127 = r358125 - r358126;
        return r358127;
}

Error

Bits error versus x

Bits error versus y

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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 *-un-lft-identity5.3

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

  4. Applied *-un-lft-identity5.3

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

  5. Applied distribute-lft-out--5.3

    \[\leadsto \color{blue}{1 \cdot \left(\frac{x}{y \cdot y} - 3\right)}\]

  6. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\frac{\frac{x}{y}}{y} - 3\right)}\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +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))