Average Error: 0.1 → 0.1
Time: 15.8s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - {x}^{3} \cdot 0.1290061377327979819096270830414141528308\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - {x}^{3} \cdot 0.1290061377327979819096270830414141528308
double f(double x) {
        double r17925 = 0.954929658551372;
        double r17926 = x;
        double r17927 = r17925 * r17926;
        double r17928 = 0.12900613773279798;
        double r17929 = r17926 * r17926;
        double r17930 = r17929 * r17926;
        double r17931 = r17928 * r17930;
        double r17932 = r17927 - r17931;
        return r17932;
}
↓
double f(double x) {
        double r17933 = 0.954929658551372;
        double r17934 = x;
        double r17935 = r17933 * r17934;
        double r17936 = 3.0;
        double r17937 = pow(r17934, r17936);
        double r17938 = 0.12900613773279798;
        double r17939 = r17937 * r17938;
        double r17940 = r17935 - r17939;
        return r17940;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))