Average Error: 4.6 → 0.1
Time: 11.9s
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 r23788104 = x;
        double r23788105 = y;
        double r23788106 = r23788105 * r23788105;
        double r23788107 = r23788104 / r23788106;
        double r23788108 = 3.0;
        double r23788109 = r23788107 - r23788108;
        return r23788109;
}
↓
double f(double x, double y) {
        double r23788110 = x;
        double r23788111 = y;
        double r23788112 = r23788110 / r23788111;
        double r23788113 = r23788112 / r23788111;
        double r23788114 = 3.0;
        double r23788115 = r23788113 - r23788114;
        return r23788115;
}

Error

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Bits error versus y

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Results

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Target

Original4.6
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.6

    \[\frac{x}{y \cdot y} - 3\]
  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 2019174 
(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))