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

Average Error: 0.1 → 0.1

Time: 18.9s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r1031060 = x;
        double r1031061 = 3.0;
        double r1031062 = r1031060 * r1031061;
        double r1031063 = y;
        double r1031064 = r1031062 * r1031063;
        double r1031065 = z;
        double r1031066 = r1031064 - r1031065;
        return r1031066;
}

↓

double f(double x, double y, double z) {
        double r1031067 = 3.0;
        double r1031068 = x;
        double r1031069 = y;
        double r1031070 = r1031068 * r1031069;
        double r1031071 = r1031067 * r1031070;
        double r1031072 = z;
        double r1031073 = r1031071 - r1031072;
        return r1031073;
}

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 *-un-lft-identity 0.1

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

7. Applied associate-*l* 0.1

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

8. Simplified 0.1

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

9. Final simplification 0.1

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

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))