Average Error: 0.2 → 0.1
Time: 3.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.95492965855137202 - \left(\left|x\right| \cdot 0.129006137732797982\right) \cdot \sqrt{x \cdot x}\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.95492965855137202 - \left(\left|x\right| \cdot 0.129006137732797982\right) \cdot \sqrt{x \cdot x}\right)
double code(double x) {
	return ((0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x)));
}
↓
double code(double x) {
	return (x * (0.954929658551372 - ((fabs(x) * 0.12900613773279798) * sqrt((x * x)))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Simplified0.1

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied associate-*r*0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020066 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))