Average Error: 0.3 → 0.3
Time: 1.2s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{0.333333333333333315 \cdot x}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{0.333333333333333315 \cdot x}{y}
double code(double x, double y) {
	return (x / (y * 3.0));
}
↓
double code(double x, double y) {
	return ((0.3333333333333333 * 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

Original0.3
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

    \[\leadsto \color{blue}{0.333333333333333315 \cdot \frac{x}{y}}\]
  3. Using strategy rm

  4. Applied associate-*r/0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))