Average Error: 0.1 → 0.1
Time: 24.4s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.9549296585513720181381813745247200131416 + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.9549296585513720181381813745247200131416 + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)
double f(double x) {
        double r17353 = 0.954929658551372;
        double r17354 = x;
        double r17355 = r17353 * r17354;
        double r17356 = 0.12900613773279798;
        double r17357 = r17354 * r17354;
        double r17358 = r17357 * r17354;
        double r17359 = r17356 * r17358;
        double r17360 = r17355 - r17359;
        return r17360;
}
↓
double f(double x) {
        double r17361 = x;
        double r17362 = 0.954929658551372;
        double r17363 = r17361 * r17362;
        double r17364 = 0.12900613773279798;
        double r17365 = 3.0;
        double r17366 = pow(r17361, r17365);
        double r17367 = r17364 * r17366;
        double r17368 = -r17367;
        double r17369 = r17363 + r17368;
        return r17369;
}

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 sub-neg0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))