Average Error: 0.2 → 0.4
Time: 1.3s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[0.333333333333333315 \cdot \frac{x}{y}\]
\frac{x}{y \cdot 3}
↓
0.333333333333333315 \cdot \frac{x}{y}
double code(double x, double y) {
	return ((double) (x / ((double) (y * 3.0))));
}
↓
double code(double x, double y) {
	return ((double) (0.3333333333333333 * ((double) (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

Original0.2
Target0.2
Herbie0.4
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \color{blue}{0.333333333333333315 \cdot \frac{x}{y}}\]

  3. Final simplification0.4

    \[\leadsto 0.333333333333333315 \cdot \frac{x}{y}\]

Reproduce

herbie shell --seed 2020124 
(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)))