Average Error: 0.1 → 0.1
Time: 4.8s
Precision: binary64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.954929658551372 + \left(x \cdot x\right) \cdot -0.12900613773279798\right)\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.954929658551372 + \left(x \cdot x\right) \cdot -0.12900613773279798\right)
(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))
↓
(FPCore (x)
 :precision binary64
 (* x (+ 0.954929658551372 (* (* x x) -0.12900613773279798))))
double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}
↓
double code(double x) {
	return x * (0.954929658551372 + ((x * x) * -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

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

  2. Simplified0.1

    \[\leadsto \color{blue}{0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}}\]
  3. Using strategy rm

  4. Applied unpow3_binary64_1440.1

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

  5. Applied associate-*r*_binary64_180.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x}\]
  6. Using strategy rm

  7. Applied distribute-rgt-out--_binary64_320.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2021027 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))