Average Error: 0.1 → 0.1
Time: 21.7s
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 r17424 = 0.954929658551372;
        double r17425 = x;
        double r17426 = r17424 * r17425;
        double r17427 = 0.12900613773279798;
        double r17428 = r17425 * r17425;
        double r17429 = r17428 * r17425;
        double r17430 = r17427 * r17429;
        double r17431 = r17426 - r17430;
        return r17431;
}
↓
double f(double x) {
        double r17432 = 0.954929658551372;
        double r17433 = x;
        double r17434 = r17432 * r17433;
        double r17435 = 0.12900613773279798;
        double r17436 = 3.0;
        double r17437 = pow(r17433, r17436);
        double r17438 = r17435 * r17437;
        double r17439 = r17434 - r17438;
        return r17439;
}

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 pow10.1

    \[\leadsto x \cdot \color{blue}{{\left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)}^{1}}\]

  5. Applied pow10.1

    \[\leadsto \color{blue}{{x}^{1}} \cdot {\left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)}^{1}\]

  6. Applied pow-prod-down0.1

    \[\leadsto \color{blue}{{\left(x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)\right)}^{1}}\]

  7. Simplified0.1

    \[\leadsto {\color{blue}{\left(0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)}}^{1}\]

  8. Final simplification0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]

Reproduce

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