Average Error: 10.2 → 0.3
Time: 2.3s
Precision: binary64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{1}{y}}{\frac{1}{\frac{x}{y}}}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{1}{y}}{\frac{1}{\frac{x}{y}}}
(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (/ (/ 1.0 y) (/ 1.0 (/ x y))))
double code(double x, double y) {
	return (x / ((double) (y * y)));
}
↓
double code(double x, double y) {
	return ((1.0 / y) / (1.0 / (x / 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

Original10.2
Target0.2
Herbie0.3
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.2

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

  3. Applied clear-num_binary6410.4

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

  4. Simplified0.6

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

  6. Applied div-inv_binary640.7

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

  7. Applied associate-/r*_binary640.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020210 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))