Average Error: 0.1 → 0.1
Time: 23.1s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x + \left(-{x}^{3} \cdot 0.1290061377327979819096270830414141528308\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x + \left(-{x}^{3} \cdot 0.1290061377327979819096270830414141528308\right)
double f(double x) {
        double r23914 = 0.954929658551372;
        double r23915 = x;
        double r23916 = r23914 * r23915;
        double r23917 = 0.12900613773279798;
        double r23918 = r23915 * r23915;
        double r23919 = r23918 * r23915;
        double r23920 = r23917 * r23919;
        double r23921 = r23916 - r23920;
        return r23921;
}
↓
double f(double x) {
        double r23922 = 0.954929658551372;
        double r23923 = x;
        double r23924 = r23922 * r23923;
        double r23925 = 3.0;
        double r23926 = pow(r23923, r23925);
        double r23927 = 0.12900613773279798;
        double r23928 = r23926 * r23927;
        double r23929 = -r23928;
        double r23930 = r23924 + r23929;
        return r23930;
}

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 sub-neg0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))