Average Error: 0.2 → 0.1
Time: 17.5s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot \left(x \cdot x\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot \left(x \cdot x\right)
double f(double x) {
        double r19313 = 0.954929658551372;
        double r19314 = x;
        double r19315 = r19313 * r19314;
        double r19316 = 0.12900613773279798;
        double r19317 = r19314 * r19314;
        double r19318 = r19317 * r19314;
        double r19319 = r19316 * r19318;
        double r19320 = r19315 - r19319;
        return r19320;
}
↓
double f(double x) {
        double r19321 = 0.954929658551372;
        double r19322 = x;
        double r19323 = r19321 * r19322;
        double r19324 = 0.12900613773279798;
        double r19325 = r19324 * r19322;
        double r19326 = r19322 * r19322;
        double r19327 = r19325 * r19326;
        double r19328 = r19323 - r19327;
        return r19328;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}}\]
  4. Using strategy rm

  5. Applied cube-mult0.2

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))