Average Error: 5.0 → 0.1
Time: 4.0s
Precision: binary64
Cost: 576
\[\frac{x}{y \cdot y} - 3\]
↓
\[\frac{\frac{1}{y}}{\frac{y}{x}} - 3\]
\frac{x}{y \cdot y} - 3
↓
\frac{\frac{1}{y}}{\frac{y}{x}} - 3
(FPCore (x y) :precision binary64 (- (/ x (* y y)) 3.0))
↓
(FPCore (x y) :precision binary64 (- (/ (/ 1.0 y) (/ y x)) 3.0))
double code(double x, double y) {
	return (x / (y * y)) - 3.0;
}
↓
double code(double x, double y) {
	return ((1.0 / y) / (y / x)) - 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

Original5.0
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} - 3\]

Alternatives

Alternative 1
Error0.1
Cost448
\[\frac{\frac{x}{y}}{y} - 3\]
Alternative 2
Error5.0
Cost448
\[\frac{x}{y \cdot y} - 3\]
Alternative 3
Error55.6
Cost64
\[-1\]
Alternative 4
Error62.2
Cost64
\[0\]
Alternative 5
Error62.6
Cost64
\[1\]

Error

Derivation

  1. Initial program 5.0

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

  3. Applied clear-num_binary64_62155.1

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

  4. Simplified0.1

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

  6. Applied div-inv_binary64_62130.1

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

  7. Applied associate-/r*_binary64_61600.1

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

  8. Taylor expanded around 0 0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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))