Average Error: 0.3 → 0.3
Time: 1.4s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{y}}{3}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{y}}{3}
double f(double x, double y) {
        double r837168 = x;
        double r837169 = y;
        double r837170 = 3.0;
        double r837171 = r837169 * r837170;
        double r837172 = r837168 / r837171;
        return r837172;
}
↓
double f(double x, double y) {
        double r837173 = x;
        double r837174 = y;
        double r837175 = r837173 / r837174;
        double r837176 = 3.0;
        double r837177 = r837175 / r837176;
        return r837177;
}

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

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 *-un-lft-identity0.4

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

  11. Applied *-un-lft-identity0.4

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

  12. Applied times-frac0.4

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

  13. Applied associate-*l*0.4

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

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

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

  (/ x (* y 3)))