Average Error: 5.1 → 0.1
Time: 16.5s
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 r201133 = x;
        double r201134 = y;
        double r201135 = r201134 * r201134;
        double r201136 = r201133 / r201135;
        double r201137 = 3.0;
        double r201138 = r201136 - r201137;
        return r201138;
}
↓
double f(double x, double y) {
        double r201139 = x;
        double r201140 = y;
        double r201141 = r201139 / r201140;
        double r201142 = r201141 / r201140;
        double r201143 = 3.0;
        double r201144 = r201142 - r201143;
        return r201144;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.1

    \[\frac{x}{y \cdot y} - 3\]
  2. Using strategy rm

  3. Applied *-un-lft-identity5.1

    \[\leadsto \frac{x}{y \cdot y} - \color{blue}{1 \cdot 3}\]

  4. Applied *-un-lft-identity5.1

    \[\leadsto \color{blue}{1 \cdot \frac{x}{y \cdot y}} - 1 \cdot 3\]

  5. Applied distribute-lft-out--5.1

    \[\leadsto \color{blue}{1 \cdot \left(\frac{x}{y \cdot y} - 3\right)}\]

  6. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\frac{\frac{x}{y}}{y} - 3\right)}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{x}{y}}{y} - 3\]

Reproduce

herbie shell --seed 2019304 +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))