Average Error: 0.1 → 0.1
Time: 10.0s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - \left(x \cdot \left(0.1290061377327979819096270830414141528308 \cdot x\right)\right) \cdot x\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - \left(x \cdot \left(0.1290061377327979819096270830414141528308 \cdot x\right)\right) \cdot x
double f(double x) {
        double r18749 = 0.954929658551372;
        double r18750 = x;
        double r18751 = r18749 * r18750;
        double r18752 = 0.12900613773279798;
        double r18753 = r18750 * r18750;
        double r18754 = r18753 * r18750;
        double r18755 = r18752 * r18754;
        double r18756 = r18751 - r18755;
        return r18756;
}
↓
double f(double x) {
        double r18757 = 0.954929658551372;
        double r18758 = x;
        double r18759 = r18757 * r18758;
        double r18760 = 0.12900613773279798;
        double r18761 = r18760 * r18758;
        double r18762 = r18758 * r18761;
        double r18763 = r18762 * r18758;
        double r18764 = r18759 - r18763;
        return r18764;
}

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. Using strategy rm

  3. Applied associate-*r*0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))