Average Error: 4.8 → 0.1
Time: 8.0s
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 r277132 = x;
        double r277133 = y;
        double r277134 = r277133 * r277133;
        double r277135 = r277132 / r277134;
        double r277136 = 3.0;
        double r277137 = r277135 - r277136;
        return r277137;
}
↓
double f(double x, double y) {
        double r277138 = x;
        double r277139 = y;
        double r277140 = r277138 / r277139;
        double r277141 = r277140 / r277139;
        double r277142 = 3.0;
        double r277143 = r277141 - r277142;
        return r277143;
}

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))