Average Error: 7.2 → 0.1
Time: 3.0s
Precision: binary64
\[\frac{x}{y \cdot y} \]
↓
\[\frac{-\frac{x}{y}}{-y} \]
\frac{x}{y \cdot y}
↓
\frac{-\frac{x}{y}}{-y}

(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (/ (- (/ x y)) (- y)))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	return -(x / y) / -y;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.2
Target0.1
Herbie0.1
\[\frac{\frac{x}{y}}{y} \]

Derivation

  1. Initial program 7.2

    \[\frac{x}{y \cdot y} \]

  2. Applied *-un-lft-identity_binary647.2

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

  3. Applied times-frac_binary640.2

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

  4. Applied associate-*r/_binary640.2

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

  5. Applied frac-2neg_binary640.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))