Average Error: 10.3 → 0.2
Time: 1.5s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{1}{y}}{\frac{y}{x}}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{1}{y}}{\frac{y}{x}}
double code(double x, double y) {
	return ((double) (x / ((double) (y * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 / y)) / ((double) (y / x))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 10.3

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

  3. Applied *-un-lft-identity10.3

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

  4. Applied times-frac0.2

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

  6. Applied clear-num0.3

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

  7. Applied un-div-inv0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))