Average Error: 5.3 → 0.1
Time: 19.5s
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 r139995 = x;
        double r139996 = y;
        double r139997 = r139996 * r139996;
        double r139998 = r139995 / r139997;
        double r139999 = 3.0;
        double r140000 = r139998 - r139999;
        return r140000;
}
↓
double f(double x, double y) {
        double r140001 = x;
        double r140002 = y;
        double r140003 = r140001 / r140002;
        double r140004 = r140003 / r140002;
        double r140005 = 3.0;
        double r140006 = r140004 - r140005;
        return r140006;
}

Error

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Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

    \[\frac{x}{y \cdot y} - 3\]
  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 2019326 +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))