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

Average Error: 0.1 → 0.1

Time: 7.6s

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 r823154 = x;
        double r823155 = 3.0;
        double r823156 = r823154 * r823155;
        double r823157 = y;
        double r823158 = r823156 * r823157;
        double r823159 = z;
        double r823160 = r823158 - r823159;
        return r823160;
}

↓

double f(double x, double y, double z) {
        double r823161 = x;
        double r823162 = y;
        double r823163 = r823161 * r823162;
        double r823164 = 3.0;
        double r823165 = r823163 * r823164;
        double r823166 = z;
        double r823167 = r823165 - r823166;
        return r823167;
}

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. Using strategy rm

5. Applied pow1 0.1

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

6. Applied pow1 0.1

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

7. Applied pow-prod-down 0.1

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

8. Applied pow1 0.1

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

9. Applied pow-prod-down 0.1

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

10. Simplified 0.1

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

11. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020045 +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))