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

Average Error: 0.2 → 0.1

Time: 11.2s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r872302 = x;
        double r872303 = 3.0;
        double r872304 = r872302 * r872303;
        double r872305 = y;
        double r872306 = r872304 * r872305;
        double r872307 = z;
        double r872308 = r872306 - r872307;
        return r872308;
}

↓

double f(double x, double y, double z) {
        double r872309 = x;
        double r872310 = 3.0;
        double r872311 = y;
        double r872312 = r872310 * r872311;
        double r872313 = r872309 * r872312;
        double r872314 = z;
        double r872315 = r872313 - r872314;
        return r872315;
}

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. Final simplification 0.1

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

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))