Average Error: 10.2 → 0.2
Time: 2.2s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{x}{y} \cdot \frac{1}{y}\]
\frac{x}{y \cdot y}
↓
\frac{x}{y} \cdot \frac{1}{y}
double code(double x, double y) {
	return (x / (y * y));
}
↓
double code(double x, double y) {
	return ((x / y) * (1.0 / 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
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

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 div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020058 +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)))