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

Average Error: 0.3 → 0.2

Time: 12.9s

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 r968526 = x;
        double r968527 = y;
        double r968528 = 3.0;
        double r968529 = r968527 * r968528;
        double r968530 = r968526 / r968529;
        return r968530;
}

↓

double f(double x, double y) {
        double r968531 = x;
        double r968532 = 3.0;
        double r968533 = r968531 / r968532;
        double r968534 = y;
        double r968535 = r968533 / r968534;
        return r968535;
}

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 *-un-lft-identity 0.3

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

8. Applied times-frac 0.3

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

9. Applied associate-*l* 0.3

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

10. Simplified 0.2

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

11. Final simplification 0.2

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

Reproduce

herbie shell --seed 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)))