Average Error: 4.8 → 0.1
Time: 6.8s
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 r228295 = x;
        double r228296 = y;
        double r228297 = r228296 * r228296;
        double r228298 = r228295 / r228297;
        double r228299 = 3.0;
        double r228300 = r228298 - r228299;
        return r228300;
}
↓
double f(double x, double y) {
        double r228301 = x;
        double r228302 = y;
        double r228303 = r228301 / r228302;
        double r228304 = r228303 / r228302;
        double r228305 = 3.0;
        double r228306 = r228304 - r228305;
        return r228306;
}

Error

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Bits error versus y

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Results

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Target

Original4.8
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.8

    \[\frac{x}{y \cdot y} - 3\]
  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 2019194 
(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))