Average Error: 0.1 → 0.1
Time: 18.7s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.9549296585513720181381813745247200131416 - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot x\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.9549296585513720181381813745247200131416 - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot x\right)
double f(double x) {
        double r21872 = 0.954929658551372;
        double r21873 = x;
        double r21874 = r21872 * r21873;
        double r21875 = 0.12900613773279798;
        double r21876 = r21873 * r21873;
        double r21877 = r21876 * r21873;
        double r21878 = r21875 * r21877;
        double r21879 = r21874 - r21878;
        return r21879;
}
↓
double f(double x) {
        double r21880 = x;
        double r21881 = 0.954929658551372;
        double r21882 = 0.12900613773279798;
        double r21883 = r21882 * r21880;
        double r21884 = r21883 * r21880;
        double r21885 = r21881 - r21884;
        double r21886 = r21880 * r21885;
        return r21886;
}

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. Using strategy rm

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))