Average Error: 0.1 → 0.1
Time: 10.8s
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 r21354 = 0.954929658551372;
        double r21355 = x;
        double r21356 = r21354 * r21355;
        double r21357 = 0.12900613773279798;
        double r21358 = r21355 * r21355;
        double r21359 = r21358 * r21355;
        double r21360 = r21357 * r21359;
        double r21361 = r21356 - r21360;
        return r21361;
}
↓
double f(double x) {
        double r21362 = 0.954929658551372;
        double r21363 = x;
        double r21364 = r21362 * r21363;
        double r21365 = 0.12900613773279798;
        double r21366 = 3.0;
        double r21367 = pow(r21363, r21366);
        double r21368 = r21365 * r21367;
        double r21369 = r21364 - r21368;
        return r21369;
}

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 2019174 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))