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

Average Error: 0.1 → 0.1

Time: 19.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(x \cdot 3\right) \cdot y - z\]

↓

\[\left(x \cdot y\right) \cdot 3 - z\]

C

double f(double x, double y, double z) {
        double r841114 = x;
        double r841115 = 3.0;
        double r841116 = r841114 * r841115;
        double r841117 = y;
        double r841118 = r841116 * r841117;
        double r841119 = z;
        double r841120 = r841118 - r841119;
        return r841120;
}

↓

double f(double x, double y, double z) {
        double r841121 = x;
        double r841122 = y;
        double r841123 = r841121 * r841122;
        double r841124 = 3.0;
        double r841125 = r841123 * r841124;
        double r841126 = z;
        double r841127 = r841125 - r841126;
        return r841127;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

1. Initial program 0.1

   \[\left(x \cdot 3\right) \cdot y - z\]
2. Using strategy rm

3. Applied associate-*l* 0.1

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

4. Simplified 0.1

   \[\leadsto x \cdot \color{blue}{\left(y \cdot 3\right)} - z\]
5. Using strategy rm

6. Applied pow1 0.1

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

7. Applied pow1 0.1

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

8. Applied pow-prod-down 0.1

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

9. Applied pow1 0.1

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

10. Applied pow-prod-down 0.1

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

11. Simplified 0.1

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

12. Final simplification 0.1

    \[\leadsto \left(x \cdot y\right) \cdot 3 - z\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3 y)) z)

  (- (* (* x 3) y) z))