Average Error: 5.2 → 0.1
Time: 31.3s
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 r275140 = x;
        double r275141 = y;
        double r275142 = r275141 * r275141;
        double r275143 = r275140 / r275142;
        double r275144 = 3.0;
        double r275145 = r275143 - r275144;
        return r275145;
}
↓
double f(double x, double y) {
        double r275146 = x;
        double r275147 = y;
        double r275148 = r275146 / r275147;
        double r275149 = r275148 / r275147;
        double r275150 = 3.0;
        double r275151 = r275149 - r275150;
        return r275151;
}

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 2019303 +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))