Average Error: 0.3 → 0.2
Time: 12.8s
Precision: 64
\[\frac{x}{y \cdot 3.0}\]
↓
\[\frac{\frac{x}{3.0}}{y}\]
\frac{x}{y \cdot 3.0}
↓
\frac{\frac{x}{3.0}}{y}
double f(double x, double y) {
        double r31364297 = x;
        double r31364298 = y;
        double r31364299 = 3.0;
        double r31364300 = r31364298 * r31364299;
        double r31364301 = r31364297 / r31364300;
        return r31364301;
}
↓
double f(double x, double y) {
        double r31364302 = x;
        double r31364303 = 3.0;
        double r31364304 = r31364302 / r31364303;
        double r31364305 = y;
        double r31364306 = r31364304 / r31364305;
        return r31364306;
}

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
\[\frac{\frac{x}{y}}{3.0}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3.0}\]
  2. Using strategy rm

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

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot 3.0}\]

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3.0}}\]
  5. Using strategy rm

  6. Applied associate-*l/0.2

    \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{3.0}}{y}}\]

  7. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{x}{3.0}}}{y}\]

  8. Final simplification0.2

    \[\leadsto \frac{\frac{x}{3.0}}{y}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))