Rosa's Benchmark

Average Error: 0.1 → 0.2

Time: 1.7s

Precision: binary64

Math

\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[x \cdot \left(0.95492965855137202 - \sqrt{0.129006137732797982} \cdot \left(\sqrt{0.129006137732797982} \cdot \left(x \cdot x\right)\right)\right)\]

C

double code(double x) {
	return ((double) (((double) (0.954929658551372 * x)) - ((double) (0.12900613773279798 * ((double) (((double) (x * x)) * x))))));
}

↓

double code(double x) {
	return ((double) (x * ((double) (0.954929658551372 - ((double) (((double) sqrt(0.12900613773279798)) * ((double) (((double) sqrt(0.12900613773279798)) * ((double) (x * x))))))))));
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{x \cdot \left(0.95492965855137202 - 0.129006137732797982 \cdot \left(x \cdot x\right)\right)}\]
3. Using strategy rm

4. Applied add-sqr-sqrt 0.1

   \[\leadsto x \cdot \left(0.95492965855137202 - \color{blue}{\left(\sqrt{0.129006137732797982} \cdot \sqrt{0.129006137732797982}\right)} \cdot \left(x \cdot x\right)\right)\]

5. Applied associate-*l* 0.2

   \[\leadsto x \cdot \left(0.95492965855137202 - \color{blue}{\sqrt{0.129006137732797982} \cdot \left(\sqrt{0.129006137732797982} \cdot \left(x \cdot x\right)\right)}\right)\]

6. Final simplification 0.2

   \[\leadsto x \cdot \left(0.95492965855137202 - \sqrt{0.129006137732797982} \cdot \left(\sqrt{0.129006137732797982} \cdot \left(x \cdot x\right)\right)\right)\]

Reproduce

herbie shell --seed 2020173 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))