Average Error: 0.2 → 0.2
Time: 1.3s
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 r911191 = x;
        double r911192 = y;
        double r911193 = 3.0;
        double r911194 = r911192 * r911193;
        double r911195 = r911191 / r911194;
        return r911195;
}
↓
double f(double x, double y) {
        double r911196 = x;
        double r911197 = 3.0;
        double r911198 = r911196 / r911197;
        double r911199 = y;
        double r911200 = r911198 / r911199;
        return r911200;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.2

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

  3. Applied *-un-lft-identity0.2

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

  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

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

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

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

  8. Applied times-frac0.3

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

  9. Applied associate-*l*0.3

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))