Average Error: 5.2 → 0.1
Time: 9.3s
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 r255061 = x;
        double r255062 = y;
        double r255063 = r255062 * r255062;
        double r255064 = r255061 / r255063;
        double r255065 = 3.0;
        double r255066 = r255064 - r255065;
        return r255066;
}
↓
double f(double x, double y) {
        double r255067 = x;
        double r255068 = y;
        double r255069 = r255067 / r255068;
        double r255070 = r255069 / r255068;
        double r255071 = 3.0;
        double r255072 = r255070 - r255071;
        return r255072;
}

Error

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Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

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

  3. Applied associate-/r*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(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))