Average Error: 10.1 → 0.2
Time: 2.1s
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

Original10.1
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y} \]

Derivation

  1. Initial program 10.1

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

  2. Applied *-un-lft-identity_binary6410.1

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

  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 *-un-lft-identity_binary640.2

    \[\leadsto \frac{\color{blue}{\left(1 \cdot \frac{1}{y}\right)} \cdot x}{y} \]

  6. Applied associate-*l*_binary640.2

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\frac{1}{y} \cdot x\right)}}{y} \]

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2021280 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))