Average Error: 0.3 → 0.2
Time: 2.1s
Precision: binary64
Cost: 320
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y}\]
\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
\[\frac{\frac{x}{y}}{3}\]

Alternatives

Alternative 1
Error0.3
Cost320
\[\frac{\frac{x}{y}}{3}\]
Alternative 2
Error53.0
Cost64
\[0\]
Alternative 3
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.3

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

  3. Applied *-un-lft-identity_binary64_212200.3

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

  4. Applied times-frac_binary64_212260.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}}\]
  5. Using strategy rm

  6. Applied associate-*l/_binary64_211630.2

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

  7. Simplified0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2021044 
(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)))