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

Average Error: 0.2 → 0.1

Time: 10.2s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r763733 = x;
        double r763734 = 3.0;
        double r763735 = r763733 * r763734;
        double r763736 = y;
        double r763737 = r763735 * r763736;
        double r763738 = z;
        double r763739 = r763737 - r763738;
        return r763739;
}

↓

double f(double x, double y, double z) {
        double r763740 = x;
        double r763741 = y;
        double r763742 = 3.0;
        double r763743 = r763741 * r763742;
        double r763744 = r763740 * r763743;
        double r763745 = z;
        double r763746 = r763744 - r763745;
        return r763746;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.2
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.2

   \[\left(x \cdot 3\right) \cdot y - z\]
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. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020046 
(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))