Average Error: 0.2 → 0.2
Time: 8.6s
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 r582115 = x;
        double r582116 = y;
        double r582117 = 3.0;
        double r582118 = r582116 * r582117;
        double r582119 = r582115 / r582118;
        return r582119;
}
↓
double f(double x, double y) {
        double r582120 = x;
        double r582121 = 3.0;
        double r582122 = r582120 / r582121;
        double r582123 = y;
        double r582124 = r582122 / r582123;
        return r582124;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-/r*0.3

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

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

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

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

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

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

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

  8. Applied times-frac0.3

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

  9. Applied times-frac0.3

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

  10. Simplified0.3

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"

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

  (/ x (* y 3.0)))