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

Average Error: 0.3 → 0.2

Time: 2.4s

Precision: 64

Math

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

↓

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

C

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

↓

double code(double x) {
	return ((6.0 - (9.0 * x)) * 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. Taylor expanded around 0 0.2

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020057 
(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))