Average Error: 0.2 → 0.2
Time: 23.7s
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 r426722 = x;
        double r426723 = y;
        double r426724 = 3.0;
        double r426725 = r426723 * r426724;
        double r426726 = r426722 / r426725;
        return r426726;
}
↓
double f(double x, double y) {
        double r426727 = x;
        double r426728 = 3.0;
        double r426729 = r426727 / r426728;
        double r426730 = y;
        double r426731 = r426729 / r426730;
        return r426731;
}

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 *-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 add-sqr-sqrt0.3

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

  8. Applied times-frac0.3

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

  9. Applied associate-*l*0.3

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 +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)))