Average Error: 10.2 → 0.2
Time: 15.0s
Precision: binary64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{1}{y}}{\frac{y}{x}}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{1}{y}}{\frac{y}{x}}
double code(double x, double y) {
	return (x / ((double) (y * y)));
}
↓
double code(double x, double y) {
	return ((1.0 / y) / (y / x));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 10.2

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

  3. Applied associate-/r*0.2

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

  5. Applied clear-num0.6

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

  6. Simplified0.6

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

  8. Applied associate-/r*0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))