Average Error: 0.2 → 0.1
Time: 15.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \frac{2150310427208497}{2251799813685248} - \frac{4647935950575487}{36028797018963968} \cdot {x}^{3}\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \frac{2150310427208497}{2251799813685248} - \frac{4647935950575487}{36028797018963968} \cdot {x}^{3}
double f(double x) {
        double r34679 = 0.954929658551372;
        double r34680 = x;
        double r34681 = r34679 * r34680;
        double r34682 = 0.12900613773279798;
        double r34683 = r34680 * r34680;
        double r34684 = r34683 * r34680;
        double r34685 = r34682 * r34684;
        double r34686 = r34681 - r34685;
        return r34686;
}
↓
double f(double x) {
        double r34687 = x;
        double r34688 = 2150310427208497.0;
        double r34689 = 2251799813685248.0;
        double r34690 = r34688 / r34689;
        double r34691 = r34687 * r34690;
        double r34692 = 4647935950575487.0;
        double r34693 = 3.602879701896397e+16;
        double r34694 = r34692 / r34693;
        double r34695 = 3.0;
        double r34696 = pow(r34687, r34695);
        double r34697 = r34694 * r34696;
        double r34698 = r34691 - r34697;
        return r34698;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(\frac{2150310427208497}{2251799813685248} - \frac{4647935950575487}{36028797018963968} \cdot \left(x \cdot x\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.1

    \[\leadsto x \cdot \color{blue}{\left(\frac{2150310427208497}{2251799813685248} + \left(-\frac{4647935950575487}{36028797018963968} \cdot \left(x \cdot x\right)\right)\right)}\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{x \cdot \frac{2150310427208497}{2251799813685248} + x \cdot \left(-\frac{4647935950575487}{36028797018963968} \cdot \left(x \cdot x\right)\right)}\]

  6. Simplified0.1

    \[\leadsto x \cdot \frac{2150310427208497}{2251799813685248} + \color{blue}{\left(-\frac{4647935950575487}{36028797018963968} \cdot {x}^{3}\right)}\]

  7. Final simplification0.1

    \[\leadsto x \cdot \frac{2150310427208497}{2251799813685248} - \frac{4647935950575487}{36028797018963968} \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))