Average Error: 5.1 → 0.1
Time: 3.3s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{\frac{x}{y}}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{\frac{x}{y}}} - 3
double f(double x, double y) {
        double r235958 = x;
        double r235959 = y;
        double r235960 = r235959 * r235959;
        double r235961 = r235958 / r235960;
        double r235962 = 3.0;
        double r235963 = r235961 - r235962;
        return r235963;
}
↓
double f(double x, double y) {
        double r235964 = 1.0;
        double r235965 = y;
        double r235966 = x;
        double r235967 = r235966 / r235965;
        double r235968 = r235965 / r235967;
        double r235969 = r235964 / r235968;
        double r235970 = 3.0;
        double r235971 = r235969 - r235970;
        return r235971;
}

Error

Bits error versus x

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 associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3\]
  4. Using strategy rm

  5. Applied clear-num0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 +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))