Average Error: 0.2 → 0.1
Time: 18.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}
double f(double x) {
        double r20691 = 0.954929658551372;
        double r20692 = x;
        double r20693 = r20691 * r20692;
        double r20694 = 0.12900613773279798;
        double r20695 = r20692 * r20692;
        double r20696 = r20695 * r20692;
        double r20697 = r20694 * r20696;
        double r20698 = r20693 - r20697;
        return r20698;
}
↓
double f(double x) {
        double r20699 = 0.954929658551372;
        double r20700 = x;
        double r20701 = r20699 * r20700;
        double r20702 = 0.12900613773279798;
        double r20703 = 3.0;
        double r20704 = pow(r20700, r20703);
        double r20705 = r20702 * r20704;
        double r20706 = r20701 - r20705;
        return r20706;
}

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 *-un-lft-identity0.1

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

  5. Applied associate-*l*0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))