Average Error: 0.1 → 0.1
Time: 9.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)
double f(double x) {
        double r18430 = 0.954929658551372;
        double r18431 = x;
        double r18432 = r18430 * r18431;
        double r18433 = 0.12900613773279798;
        double r18434 = r18431 * r18431;
        double r18435 = r18434 * r18431;
        double r18436 = r18433 * r18435;
        double r18437 = r18432 - r18436;
        return r18437;
}
↓
double f(double x) {
        double r18438 = 0.954929658551372;
        double r18439 = x;
        double r18440 = r18438 * r18439;
        double r18441 = 0.12900613773279798;
        double r18442 = 3.0;
        double r18443 = pow(r18439, r18442);
        double r18444 = r18441 * r18443;
        double r18445 = -r18444;
        double r18446 = r18440 + r18445;
        return r18446;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))