Average Error: 4.8 → 0.1
Time: 2.0s
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

(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

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. Applied *-un-lft-identity_binary644.8

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

  3. Applied times-frac_binary640.1

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

  4. Applied associate-*r/_binary640.1

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

  5. Applied associate-/l*_binary640.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021313 
(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))