Average Error: 4.8 → 0.1
Time: 3.6s
Precision: binary64
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{x}{y}}{y} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{x}{y}}{y} - 3
(FPCore (x y) :precision binary64 (- (/ x (* y y)) 3.0))
↓
(FPCore (x y) :precision binary64 (- (/ (/ x y) y) 3.0))
double code(double x, double y) {
	return (x / (y * y)) - 3.0;
}
↓
double code(double x, double y) {
	return ((x / y) / y) - 3.0;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 clear-num_binary644.8

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

  4. Simplified0.1

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

  6. Applied associate-/r/_binary640.1

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

  7. Applied add-sqr-sqrt_binary640.1

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

  8. Applied times-frac_binary640.1

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

  9. Simplified0.1

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

  10. Simplified0.1

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

  12. Applied associate-*r/_binary640.1

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

  13. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021110 
(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))