Average Error: 5.2 → 0.1
Time: 1.9s
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 r274569 = x;
        double r274570 = y;
        double r274571 = r274570 * r274570;
        double r274572 = r274569 / r274571;
        double r274573 = 3.0;
        double r274574 = r274572 - r274573;
        return r274574;
}
↓
double f(double x, double y) {
        double r274575 = 1.0;
        double r274576 = y;
        double r274577 = x;
        double r274578 = r274576 / r274577;
        double r274579 = r274578 * r274576;
        double r274580 = r274575 / r274579;
        double r274581 = 3.0;
        double r274582 = r274580 - r274581;
        return r274582;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 5.2

    \[\frac{x}{y \cdot y} - 3\]
  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 associate-/r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 
(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))