Average Error: 0.1 → 0.1
Time: 2.2s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - 1 \cdot \left({x}^{3} \cdot 0.1290061377327979819096270830414141528308\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - 1 \cdot \left({x}^{3} \cdot 0.1290061377327979819096270830414141528308\right)
double f(double x) {
        double r20101 = 0.954929658551372;
        double r20102 = x;
        double r20103 = r20101 * r20102;
        double r20104 = 0.12900613773279798;
        double r20105 = r20102 * r20102;
        double r20106 = r20105 * r20102;
        double r20107 = r20104 * r20106;
        double r20108 = r20103 - r20107;
        return r20108;
}
↓
double f(double x) {
        double r20109 = 0.954929658551372;
        double r20110 = x;
        double r20111 = r20109 * r20110;
        double r20112 = 1.0;
        double r20113 = 3.0;
        double r20114 = pow(r20110, r20113);
        double r20115 = 0.12900613773279798;
        double r20116 = r20114 * r20115;
        double r20117 = r20112 * r20116;
        double r20118 = r20111 - r20117;
        return r20118;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-*l*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))