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

Average Error: 0.2 → 0.2

Time: 2.5s

Precision: 64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x

Target

Original	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

2. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

3. Simplified 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020121 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))