Average Error: 5.3 → 0.1
Time: 2.4s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{\frac{y}{x} \cdot y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{\frac{y}{x} \cdot y} - 3
double f(double x, double y) {
        double r258069 = x;
        double r258070 = y;
        double r258071 = r258070 * r258070;
        double r258072 = r258069 / r258071;
        double r258073 = 3.0;
        double r258074 = r258072 - r258073;
        return r258074;
}
↓
double f(double x, double y) {
        double r258075 = 1.0;
        double r258076 = y;
        double r258077 = x;
        double r258078 = r258076 / r258077;
        double r258079 = r258078 * r258076;
        double r258080 = r258075 / r258079;
        double r258081 = 3.0;
        double r258082 = r258080 - r258081;
        return r258082;
}

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. Using strategy rm

  5. Applied *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{y}{\frac{x}{y}}}} - 3\]
  9. Using strategy rm

  10. Applied associate-/r/0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 +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))