Average Error: 4.7 → 0.1
Time: 1.9s
Precision: binary64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{y}}{\frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{y}}{\frac{y}{x}} - 3
double code(double x, double y) {
	return ((double) (((double) (x / ((double) (y * y)))) - 3.0));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (1.0 / y)) / ((double) (y / x)))) - 3.0));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original4.7
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Derivation

  1. Initial program 4.7

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

  3. Applied clear-num4.7

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

  4. Simplified0.1

    \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{y}{x}}} - 3\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020184 
(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))