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

Average Error: 0.3 → 0.2

Time: 18.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r54014 = x;
        double r54015 = y;
        double r54016 = 3.0;
        double r54017 = r54015 * r54016;
        double r54018 = r54014 / r54017;
        return r54018;
}

↓

double f(double x, double y) {
        double r54019 = x;
        double r54020 = 3.0;
        double r54021 = r54019 / r54020;
        double r54022 = y;
        double r54023 = r54021 / r54022;
        return r54023;
}

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 *-un-lft-identity 0.3

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

7. Applied add-cube-cbrt 0.3

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

8. Applied times-frac 0.3

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

9. Applied associate-*l* 0.3

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

10. Simplified 0.2

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

11. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019310 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

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

  (/ x (* y 3)))