Average Error: 0.1 → 0.1
Time: 14.8s
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 r21746 = 0.954929658551372;
        double r21747 = x;
        double r21748 = r21746 * r21747;
        double r21749 = 0.12900613773279798;
        double r21750 = r21747 * r21747;
        double r21751 = r21750 * r21747;
        double r21752 = r21749 * r21751;
        double r21753 = r21748 - r21752;
        return r21753;
}
↓
double f(double x) {
        double r21754 = x;
        double r21755 = 0.954929658551372;
        double r21756 = 0.12900613773279798;
        double r21757 = r21756 * r21754;
        double r21758 = r21757 * r21754;
        double r21759 = r21755 - r21758;
        double r21760 = r21754 * r21759;
        return r21760;
}

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 2019298 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))