Average Error: 10.3 → 0.2
Time: 2.0s
Precision: binary64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{1}{y} \cdot \frac{x}{y}\]
\frac{x}{y \cdot y}
↓
\frac{1}{y} \cdot \frac{x}{y}
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) (x / y))));
}

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

Original10.3
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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020173 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))