Average Error: 5.0 → 0.1
Time: 14.6s
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 r14621942 = x;
        double r14621943 = y;
        double r14621944 = r14621943 * r14621943;
        double r14621945 = r14621942 / r14621944;
        double r14621946 = 3.0;
        double r14621947 = r14621945 - r14621946;
        return r14621947;
}
↓
double f(double x, double y) {
        double r14621948 = x;
        double r14621949 = y;
        double r14621950 = r14621948 / r14621949;
        double r14621951 = r14621950 / r14621949;
        double r14621952 = 3.0;
        double r14621953 = r14621951 - r14621952;
        return r14621953;
}

Error

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Bits error versus y

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Results

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Target

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.0

    \[\frac{x}{y \cdot y} - 3\]
  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 2019172 
(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))