Average Error: 0.3 → 0.2
Time: 19.1s
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 r495522 = x;
        double r495523 = y;
        double r495524 = 3.0;
        double r495525 = r495523 * r495524;
        double r495526 = r495522 / r495525;
        return r495526;
}
↓
double f(double x, double y) {
        double r495527 = x;
        double r495528 = 3.0;
        double r495529 = r495527 / r495528;
        double r495530 = y;
        double r495531 = r495529 / r495530;
        return r495531;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.3
Target0.2
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 pow10.3

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

  7. Applied pow10.3

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

  8. Applied pow-prod-down0.3

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))