Average Error: 5.1 → 0.1
Time: 16.4s
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 r17029772 = x;
        double r17029773 = y;
        double r17029774 = r17029773 * r17029773;
        double r17029775 = r17029772 / r17029774;
        double r17029776 = 3.0;
        double r17029777 = r17029775 - r17029776;
        return r17029777;
}
↓
double f(double x, double y) {
        double r17029778 = x;
        double r17029779 = y;
        double r17029780 = r17029778 / r17029779;
        double r17029781 = r17029780 / r17029779;
        double r17029782 = 3.0;
        double r17029783 = r17029781 - r17029782;
        return r17029783;
}

Error

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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 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 2019171 
(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))