Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F

Average Error: 0.2 → 0.2

Time: 12.5s

Precision: 64

Math

\[\left(x \cdot 3\right) \cdot x\]

↓

\[3 \cdot \left(x \cdot x\right)\]

C

double f(double x) {
        double r214198 = x;
        double r214199 = 3.0;
        double r214200 = r214198 * r214199;
        double r214201 = r214200 * r214198;
        return r214201;
}

↓

double f(double x) {
        double r214202 = 3.0;
        double r214203 = x;
        double r214204 = r214203 * r214203;
        double r214205 = r214202 * r214204;
        return r214205;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\left(x \cdot 3\right) \cdot x\]

2. Simplified 0.2

   \[\leadsto \color{blue}{x \cdot \left(x \cdot 3\right)}\]
3. Using strategy rm

4. Applied pow1 0.2

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

5. Applied pow1 0.2

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

6. Applied pow-prod-down 0.2

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

7. Applied pow1 0.2

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

8. Applied pow-prod-down 0.2

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

9. Simplified 0.2

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

10. Final simplification 0.2

    \[\leadsto 3 \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  (* (* x 3.0) x))