Average Error: 0.1 → 0.1
Time: 2.5s
Precision: binary64
Cost: 6912
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}
(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))
↓
(FPCore (x)
 :precision binary64
 (- (* x 0.954929658551372) (* 0.12900613773279798 (pow x 3.0))))
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, 3.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.1
Cost704
\[x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)\]
Alternative 2
Error0.1
Cost576
\[x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)\]
Alternative 3
Error1.2
Cost776
\[\begin{array}{l} \mathbf{if}\;x \leq -2.691175105446575 \lor \neg \left(x \leq 2.7638712165586954\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -0.12900613773279798\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.954929658551372\\ \end{array}\]
Alternative 4
Error16.7
Cost192
\[x \cdot 0.954929658551372\]
Alternative 5
Error61.1
Cost64
\[0\]
Alternative 6
Error61.7
Cost64
\[1\]

Error

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. Simplified0.1

    \[\leadsto \color{blue}{x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}}\]

  4. Final simplification0.1

    \[\leadsto x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))