Average Error: 0.3 → 0.2
Time: 1.5s
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 r846317 = x;
        double r846318 = y;
        double r846319 = 3.0;
        double r846320 = r846318 * r846319;
        double r846321 = r846317 / r846320;
        return r846321;
}
↓
double f(double x, double y) {
        double r846322 = x;
        double r846323 = 3.0;
        double r846324 = r846322 / r846323;
        double r846325 = y;
        double r846326 = r846324 / r846325;
        return r846326;
}

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 *-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 div-inv0.4

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

  7. Applied associate-*r*0.4

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

  8. Simplified0.4

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

  10. Applied associate-*l/0.3

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))