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

Average Error: 0.2 → 0.1

Time: 15.4s

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 r775701 = x;
        double r775702 = 3.0;
        double r775703 = r775701 * r775702;
        double r775704 = y;
        double r775705 = r775703 * r775704;
        double r775706 = z;
        double r775707 = r775705 - r775706;
        return r775707;
}

↓

double f(double x, double y, double z) {
        double r775708 = x;
        double r775709 = 3.0;
        double r775710 = y;
        double r775711 = r775709 * r775710;
        double r775712 = r775708 * r775711;
        double r775713 = z;
        double r775714 = r775712 - r775713;
        return r775714;
}

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 +o rules:numerics
(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))