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

Average Error: 0.3 → 0.3

Time: 1.6s

Precision: 64

Math

\[\left(x \cdot 27\right) \cdot y\]

↓

\[27 \cdot \left(x \cdot y\right)\]

C

double f(double x, double y) {
        double r236836 = x;
        double r236837 = 27.0;
        double r236838 = r236836 * r236837;
        double r236839 = y;
        double r236840 = r236838 * r236839;
        return r236840;
}

↓

double f(double x, double y) {
        double r236841 = 27.0;
        double r236842 = x;
        double r236843 = y;
        double r236844 = r236842 * r236843;
        double r236845 = r236841 * r236844;
        return r236845;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.3

   \[\left(x \cdot 27\right) \cdot y\]
2. Using strategy rm

3. Applied pow1 0.3

   \[\leadsto \left(x \cdot 27\right) \cdot \color{blue}{{y}^{1}}\]

4. Applied pow1 0.3

   \[\leadsto \left(x \cdot \color{blue}{{27}^{1}}\right) \cdot {y}^{1}\]

5. Applied pow1 0.3

   \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {27}^{1}\right) \cdot {y}^{1}\]

6. Applied pow-prod-down 0.3

   \[\leadsto \color{blue}{{\left(x \cdot 27\right)}^{1}} \cdot {y}^{1}\]

7. Applied pow-prod-down 0.3

   \[\leadsto \color{blue}{{\left(\left(x \cdot 27\right) \cdot y\right)}^{1}}\]

8. Simplified 0.3

   \[\leadsto {\color{blue}{\left(27 \cdot \left(x \cdot y\right)\right)}}^{1}\]

9. Final simplification 0.3

   \[\leadsto 27 \cdot \left(x \cdot y\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))