Average Error: 9.7 → 0.2
Time: 1.5s
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}
(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (* (/ 1.0 y) (/ x y)))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	return (1.0 / y) * (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

Original9.7
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 9.7

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

  3. Applied *-un-lft-identity_binary649.7

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

  4. Applied times-frac_binary640.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020232 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))