Average Error: 0.1 → 0.1
Time: 1.7s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\mathsf{fma}\left(x, 0.95492965855137202, {x}^{3} \cdot \left(-0.129006137732797982\right)\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
\mathsf{fma}\left(x, 0.95492965855137202, {x}^{3} \cdot \left(-0.129006137732797982\right)\right)
double code(double x) {
	return ((0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x)));
}
↓
double code(double x) {
	return fma(x, 0.954929658551372, (pow(x, 3.0) * -0.12900613773279798));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
  2. Using strategy rm

  3. Applied *-commutative0.1

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

  4. Applied fma-neg0.1

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

  5. Simplified0.1

    \[\leadsto \mathsf{fma}\left(x, 0.95492965855137202, \color{blue}{{x}^{3} \cdot \left(-0.129006137732797982\right)}\right)\]

  6. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, 0.95492965855137202, {x}^{3} \cdot \left(-0.129006137732797982\right)\right)\]

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))