Average Error: 5.4 → 0.1
Time: 3.4s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{1}}{\frac{y}{\frac{x}{y}}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{1}}{\frac{y}{\frac{x}{y}}} - 3
double f(double x, double y) {
        double r328221 = x;
        double r328222 = y;
        double r328223 = r328222 * r328222;
        double r328224 = r328221 / r328223;
        double r328225 = 3.0;
        double r328226 = r328224 - r328225;
        return r328226;
}
↓
double f(double x, double y) {
        double r328227 = 1.0;
        double r328228 = r328227 / r328227;
        double r328229 = y;
        double r328230 = x;
        double r328231 = r328230 / r328229;
        double r328232 = r328229 / r328231;
        double r328233 = r328228 / r328232;
        double r328234 = 3.0;
        double r328235 = r328233 - r328234;
        return r328235;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.4

    \[\frac{x}{y \cdot y} - 3\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 
(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))