Average Error: 0.3 → 0.3
Time: 2.0s
Precision: binary64
\[\frac{x}{y \cdot 3}\]
↓
\[x \cdot \frac{0.3333333333333333}{y}\]
\frac{x}{y \cdot 3}
↓
x \cdot \frac{0.3333333333333333}{y}
double code(double x, double y) {
	return (x / ((double) (y * 3.0)));
}
↓
double code(double x, double y) {
	return ((double) (x * (0.3333333333333333 / 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

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

Derivation

  1. Initial program 0.3

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{x}{y}}\]

  3. Simplified0.3

    \[\leadsto \color{blue}{x \cdot \frac{0.3333333333333333}{y}}\]

  4. Final simplification0.3

    \[\leadsto x \cdot \frac{0.3333333333333333}{y}\]

Reproduce

herbie shell --seed 2020199 
(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)))