Average Error: 5.1 → 0.1
Time: 12.4s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y} \cdot \frac{x}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y} \cdot \frac{x}{y} - 3
double f(double x, double y) {
        double r175112 = x;
        double r175113 = y;
        double r175114 = r175113 * r175113;
        double r175115 = r175112 / r175114;
        double r175116 = 3.0;
        double r175117 = r175115 - r175116;
        return r175117;
}
↓
double f(double x, double y) {
        double r175118 = 1.0;
        double r175119 = y;
        double r175120 = r175118 / r175119;
        double r175121 = x;
        double r175122 = r175121 / r175119;
        double r175123 = r175120 * r175122;
        double r175124 = 3.0;
        double r175125 = r175123 - r175124;
        return r175125;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied *-un-lft-identity5.1

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

  4. Applied times-frac0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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))