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

Average Error: 0.3 → 0.2

Time: 5.3s

Precision: binary64

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

Math

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]

↓

\[6 \cdot x - \left(x \cdot 9\right) \cdot x\]

C

double code(double x) {
	return ((double) (((double) (3.0 * ((double) (2.0 - ((double) (x * 3.0)))))) * x));
}

↓

double code(double x) {
	return ((double) (((double) (6.0 * x)) - ((double) (((double) (x * 9.0)) * x))));
}

Error

Bits error versus x

Target

Original	0.3
Target	0.2
Herbie	0.2

\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

1. Initial program 0.3

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

3. Applied flip-- 0.3

   \[\leadsto \left(3 \cdot \color{blue}{\frac{2 \cdot 2 - \left(x \cdot 3\right) \cdot \left(x \cdot 3\right)}{2 + x \cdot 3}}\right) \cdot x\]

4. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]
5. Using strategy rm

6. Applied unpow2 0.2

   \[\leadsto 6 \cdot x - 9 \cdot \color{blue}{\left(x \cdot x\right)}\]

7. Applied associate-*r* 0.2

   \[\leadsto 6 \cdot x - \color{blue}{\left(9 \cdot x\right) \cdot x}\]

8. Simplified 0.2

   \[\leadsto 6 \cdot x - \color{blue}{\left(x \cdot 9\right)} \cdot x\]

9. Final simplification 0.2

   \[\leadsto 6 \cdot x - \left(x \cdot 9\right) \cdot x\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

  (* (* 3.0 (- 2.0 (* x 3.0))) x))