Average Error: 0.3 → 0.3
Time: 1.7s
Precision: binary64
\[\frac{x}{y \cdot 3}\]
↓
\[x \cdot \frac{0.333333333333333315}{y}\]
\frac{x}{y \cdot 3}
↓
x \cdot \frac{0.333333333333333315}{y}
double code(double x, double y) {
	return ((double) (x / ((double) (y * 3.0))));
}
↓
double code(double x, double y) {
	return ((double) (x * ((double) (0.3333333333333333 / y))));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

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

  5. Applied *-un-lft-identity0.2

    \[\leadsto \frac{\frac{x}{y}}{\color{blue}{1 \cdot 3}}\]

  6. Applied div-inv0.3

    \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{y}}}{1 \cdot 3}\]

  7. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{\frac{1}{y}}{3}}\]

  8. Simplified0.3

    \[\leadsto \color{blue}{x} \cdot \frac{\frac{1}{y}}{3}\]

  9. Taylor expanded around 0 0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020173 
(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)))