Average Error: 4.9 → 0.1
Time: 1.8s
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 r303515 = x;
        double r303516 = y;
        double r303517 = r303516 * r303516;
        double r303518 = r303515 / r303517;
        double r303519 = 3.0;
        double r303520 = r303518 - r303519;
        return r303520;
}
↓
double f(double x, double y) {
        double r303521 = 1.0;
        double r303522 = y;
        double r303523 = x;
        double r303524 = r303522 / r303523;
        double r303525 = r303524 * r303522;
        double r303526 = r303521 / r303525;
        double r303527 = 3.0;
        double r303528 = r303526 - r303527;
        return r303528;
}

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 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 2020027 +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))