Average Error: 0.1 → 0.1
Time: 23.6s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - \left(0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right) \cdot x\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - \left(0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right) \cdot x
double f(double x) {
        double r850816 = 0.954929658551372;
        double r850817 = x;
        double r850818 = r850816 * r850817;
        double r850819 = 0.12900613773279798;
        double r850820 = r850817 * r850817;
        double r850821 = r850820 * r850817;
        double r850822 = r850819 * r850821;
        double r850823 = r850818 - r850822;
        return r850823;
}
↓
double f(double x) {
        double r850824 = 0.954929658551372;
        double r850825 = x;
        double r850826 = r850824 * r850825;
        double r850827 = 0.12900613773279798;
        double r850828 = r850825 * r850825;
        double r850829 = r850827 * r850828;
        double r850830 = r850829 * r850825;
        double r850831 = r850826 - r850830;
        return r850831;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))