Average Error: 4.8 → 0.1
Time: 2.8s
Precision: 64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{y}}{\frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{y}}{\frac{y}{x}} - 3
double f(double x, double y) {
        double r351570 = x;
        double r351571 = y;
        double r351572 = r351571 * r351571;
        double r351573 = r351570 / r351572;
        double r351574 = 3.0;
        double r351575 = r351573 - r351574;
        return r351575;
}
↓
double f(double x, double y) {
        double r351576 = 1.0;
        double r351577 = y;
        double r351578 = r351576 / r351577;
        double r351579 = x;
        double r351580 = r351577 / r351579;
        double r351581 = r351578 / r351580;
        double r351582 = 3.0;
        double r351583 = r351581 - r351582;
        return r351583;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original4.8
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.8

    \[\frac{x}{y \cdot y} - 3\]
  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. Using strategy rm

  7. Applied div-inv0.1

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

  8. Applied associate-/r*0.1

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

  9. Taylor expanded around 0 0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(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))