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

Average Error: 0.2 → 0.2

Time: 2.1s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

(FPCore (x) :precision binary64 (* (* x 3.0) x))

↓

(FPCore (x) :precision binary64 (* 3.0 (* x x)))

C

double code(double x) {
	return (x * 3.0) * x;
}

↓

double code(double x) {
	return 3.0 * (x * x);
}

Error

Bits error versus x

Alternatives

Alternative 1
Error	41.9
Cost	64

\[0\]

Alternative 2
Error	61.0
Cost	64

\[1\]

Derivation

1. Initial program 0.2

   \[\left(x \cdot 3\right) \cdot x\]
2. Using strategy rm

3. Applied add-sqr-sqrt_binary64_6238 0.4

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

4. Simplified 0.4

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

5. Simplified 0.4

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

7. Applied *-un-lft-identity_binary64_6216 0.4

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

8. Applied associate-*r*_binary64_6156 0.4

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

9. Simplified 0.3

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

11. Applied associate-*r*_binary64_6156 0.3

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

13. Applied pow1_binary64_6277 0.3

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

14. Applied pow1_binary64_6277 0.3

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

15. Applied pow-prod-down_binary64_6287 0.3

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

16. Simplified 0.2

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

17. Simplified 0.2

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

18. Final simplification 0.2

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))