Average Error: 4.8 → 0.1
Time: 2.2s
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 r245130 = x;
        double r245131 = y;
        double r245132 = r245131 * r245131;
        double r245133 = r245130 / r245132;
        double r245134 = 3.0;
        double r245135 = r245133 - r245134;
        return r245135;
}
↓
double f(double x, double y) {
        double r245136 = x;
        double r245137 = y;
        double r245138 = r245136 / r245137;
        double r245139 = r245138 / r245137;
        double r245140 = 3.0;
        double r245141 = r245139 - r245140;
        return r245141;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3)

  (- (/ x (* y y)) 3))