Average Error: 0.3 → 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

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

Derivation

  1. Initial program 0.3

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

  3. Applied clear-num_binary64_167860.7

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

  4. Simplified0.6

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

  5. Taylor expanded around 0 0.4

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020356 
(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)))