Average Error: 0.2 → 0.2
Time: 1.8s
Precision: binary64
\[\frac{x}{y \cdot 3} \]
↓
\[\frac{\frac{x}{3}}{y} \]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y}

(FPCore (x y) :precision binary64 (/ x (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (/ (/ x 3.0) y))
double code(double x, double y) {
	return x / (y * 3.0);
}
↓
double code(double x, double y) {
	return (x / 3.0) / 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

Original0.2
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{3} \]

Derivation

  1. Initial program 0.2

    \[\frac{x}{y \cdot 3} \]

  2. Applied associate-/r*_binary640.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{3}} \]

  3. Applied associate-/l/_binary640.2

    \[\leadsto \color{blue}{\frac{x}{3 \cdot y}} \]

  4. Applied associate-/r*_binary640.2

    \[\leadsto \color{blue}{\frac{\frac{x}{3}}{y}} \]

  5. Final simplification0.2

    \[\leadsto \frac{\frac{x}{3}}{y} \]

Reproduce

herbie shell --seed 2022068 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))