Average Error: 4.9 → 0.1
Time: 2.3s
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 r221569 = x;
        double r221570 = y;
        double r221571 = r221570 * r221570;
        double r221572 = r221569 / r221571;
        double r221573 = 3.0;
        double r221574 = r221572 - r221573;
        return r221574;
}
↓
double f(double x, double y) {
        double r221575 = 1.0;
        double r221576 = y;
        double r221577 = x;
        double r221578 = r221576 / r221577;
        double r221579 = r221578 * r221576;
        double r221580 = r221575 / r221579;
        double r221581 = 3.0;
        double r221582 = r221580 - r221581;
        return r221582;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.9
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.9

    \[\frac{x}{y \cdot y} - 3\]
  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 2020027 
(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))