Average Error: 0.1 → 0.1
Time: 12.5s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}
double f(double x) {
        double r18815 = 0.954929658551372;
        double r18816 = x;
        double r18817 = r18815 * r18816;
        double r18818 = 0.12900613773279798;
        double r18819 = r18816 * r18816;
        double r18820 = r18819 * r18816;
        double r18821 = r18818 * r18820;
        double r18822 = r18817 - r18821;
        return r18822;
}
↓
double f(double x) {
        double r18823 = 0.954929658551372;
        double r18824 = x;
        double r18825 = r18823 * r18824;
        double r18826 = 0.12900613773279798;
        double r18827 = 3.0;
        double r18828 = pow(r18824, r18827);
        double r18829 = r18826 * r18828;
        double r18830 = r18825 - r18829;
        return r18830;
}

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

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

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}}\]

  4. Final simplification0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))