Average Error: 5.1 → 0.1
Time: 1.6s
Precision: binary64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{1}{y \cdot \frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{1}{y \cdot \frac{y}{x}} - 3
double code(double x, double y) {
	return ((double) ((x / ((double) (y * y))) - 3.0));
}
↓
double code(double x, double y) {
	return ((double) ((1.0 / ((double) (y * (y / x)))) - 3.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 5.1

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

  3. Applied clear-num5.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020199 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))