Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, C

Average Error: 0.3 → 0.2

Time: 11.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y) {
        double r431238 = x;
        double r431239 = y;
        double r431240 = 3.0;
        double r431241 = r431239 * r431240;
        double r431242 = r431238 / r431241;
        return r431242;
}

↓

double f(double x, double y) {
        double r431243 = x;
        double r431244 = 3.0;
        double r431245 = r431243 / r431244;
        double r431246 = y;
        double r431247 = r431245 / r431246;
        return r431247;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.3
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

3. Applied *-un-lft-identity 0.3

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

4. Applied times-frac 0.3

   \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}}\]
5. Using strategy rm

6. Applied pow1 0.3

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

7. Applied pow1 0.3

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

8. Applied pow-prod-down 0.3

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

9. Simplified 0.2

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

10. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))