Average Error: 0.2 → 0.1
Time: 11.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.9549296585513720181381813745247200131416 + \left(\left(-0.1290061377327979819096270830414141528308\right) \cdot x\right) \cdot x\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.9549296585513720181381813745247200131416 + \left(\left(-0.1290061377327979819096270830414141528308\right) \cdot x\right) \cdot x\right)
double f(double x) {
        double r24698 = 0.954929658551372;
        double r24699 = x;
        double r24700 = r24698 * r24699;
        double r24701 = 0.12900613773279798;
        double r24702 = r24699 * r24699;
        double r24703 = r24702 * r24699;
        double r24704 = r24701 * r24703;
        double r24705 = r24700 - r24704;
        return r24705;
}
↓
double f(double x) {
        double r24706 = x;
        double r24707 = 0.954929658551372;
        double r24708 = 0.12900613773279798;
        double r24709 = -r24708;
        double r24710 = r24709 * r24706;
        double r24711 = r24710 * r24706;
        double r24712 = r24707 + r24711;
        double r24713 = r24706 * r24712;
        return r24713;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  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. Simplified0.1

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

  6. Final simplification0.1

    \[\leadsto x \cdot \left(0.9549296585513720181381813745247200131416 + \left(\left(-0.1290061377327979819096270830414141528308\right) \cdot x\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))