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

Average Error: 0.3 → 0.2

Time: 16.9s

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 r931866 = x;
        double r931867 = y;
        double r931868 = 3.0;
        double r931869 = r931867 * r931868;
        double r931870 = r931866 / r931869;
        return r931870;
}

↓

double f(double x, double y) {
        double r931871 = x;
        double r931872 = 3.0;
        double r931873 = r931871 / r931872;
        double r931874 = y;
        double r931875 = r931873 / r931874;
        return r931875;
}

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 associate-*l/ 0.2

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

7. Simplified 0.2

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

8. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020042 +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)))