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

Average Error: 0.3 → 0.2

Time: 1.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r644963 = x;
        double r644964 = y;
        double r644965 = 3.0;
        double r644966 = r644964 * r644965;
        double r644967 = r644963 / r644966;
        return r644967;
}

↓

double f(double x, double y) {
        double r644968 = x;
        double r644969 = 3.0;
        double r644970 = r644968 / r644969;
        double r644971 = y;
        double r644972 = r644970 / r644971;
        double r644973 = 1.0;
        double r644974 = sqrt(r644973);
        double r644975 = r644972 * r644974;
        return r644975;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.2
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 *-un-lft-identity 0.3

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

7. Applied add-sqr-sqrt 0.3

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

8. Applied times-frac 0.3

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

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. Simplified 0.2

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

11. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020002 +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)))