Average Error: 0.3 → 0.2
Time: 2.3s
Precision: binary64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
↓
\[x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right) \]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right)

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))
↓
(FPCore (x)
 :precision binary64
 (* x (- 0.954929658551372 (* 0.12900613773279798 (pow x 2.0)))))
double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}
↓
double code(double x) {
	return x * (0.954929658551372 - (0.12900613773279798 * pow(x, 2.0)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(x \cdot x, -0.12900613773279798, 0.954929658551372\right)} \]

  3. Taylor expanded in x around 0 0.2

    \[\leadsto x \cdot \color{blue}{\left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right)} \]

  4. Final simplification0.2

    \[\leadsto x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right) \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))