Average Error: 0.3 → 0.2
Time: 1.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y}
double f(double x, double y) {
        double r659464 = x;
        double r659465 = y;
        double r659466 = 3.0;
        double r659467 = r659465 * r659466;
        double r659468 = r659464 / r659467;
        return r659468;
}
↓
double f(double x, double y) {
        double r659469 = x;
        double r659470 = 3.0;
        double r659471 = r659469 / r659470;
        double r659472 = y;
        double r659473 = r659471 / r659472;
        return r659473;
}

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

Derivation

  1. Initial program 0.3

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

  3. Applied *-un-lft-identity0.3

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

  4. Applied times-frac0.3

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

  6. Applied *-un-lft-identity0.3

    \[\leadsto \color{blue}{\left(1 \cdot \frac{1}{y}\right)} \cdot \frac{x}{3}\]

  7. Applied associate-*l*0.3

    \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{y} \cdot \frac{x}{3}\right)}\]

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))