Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982
double f(double x) {
        double r20604 = 0.954929658551372;
        double r20605 = x;
        double r20606 = r20604 * r20605;
        double r20607 = 0.12900613773279798;
        double r20608 = r20605 * r20605;
        double r20609 = r20608 * r20605;
        double r20610 = r20607 * r20609;
        double r20611 = r20606 - r20610;
        return r20611;
}
↓
double f(double x) {
        double r20612 = 0.954929658551372;
        double r20613 = x;
        double r20614 = r20612 * r20613;
        double r20615 = 3.0;
        double r20616 = pow(r20613, r20615);
        double r20617 = 0.12900613773279798;
        double r20618 = r20616 * r20617;
        double r20619 = r20614 - r20618;
        return r20619;
}

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. Taylor expanded around 0 0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{0.129006137732797982 \cdot {x}^{3}}\]

  3. Simplified0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{{x}^{3} \cdot 0.129006137732797982}\]

  4. Final simplification0.1

    \[\leadsto 0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))