Average Error: 0.1 → 0.1
Time: 21.2s
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 r23832 = 0.954929658551372;
        double r23833 = x;
        double r23834 = r23832 * r23833;
        double r23835 = 0.12900613773279798;
        double r23836 = r23833 * r23833;
        double r23837 = r23836 * r23833;
        double r23838 = r23835 * r23837;
        double r23839 = r23834 - r23838;
        return r23839;
}
↓
double f(double x) {
        double r23840 = 0.954929658551372;
        double r23841 = x;
        double r23842 = r23840 * r23841;
        double r23843 = 3.0;
        double r23844 = pow(r23841, r23843);
        double r23845 = 0.12900613773279798;
        double r23846 = r23844 * r23845;
        double r23847 = r23842 - r23846;
        return r23847;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \color{blue}{\left(1 \cdot 0.1290061377327979819096270830414141528308\right)} \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  4. Applied associate-*l*0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \color{blue}{1 \cdot \left(0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\]

  5. Simplified0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - 1 \cdot \color{blue}{\left({x}^{3} \cdot 0.1290061377327979819096270830414141528308\right)}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))