Average Error: 0.1 → 0.1
Time: 11.4s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.9549296585513720181381813745247200131416 - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot x\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.9549296585513720181381813745247200131416 - \left(0.1290061377327979819096270830414141528308 \cdot x\right) \cdot x\right)
double f(double x) {
        double r17976 = 0.954929658551372;
        double r17977 = x;
        double r17978 = r17976 * r17977;
        double r17979 = 0.12900613773279798;
        double r17980 = r17977 * r17977;
        double r17981 = r17980 * r17977;
        double r17982 = r17979 * r17981;
        double r17983 = r17978 - r17982;
        return r17983;
}
↓
double f(double x) {
        double r17984 = x;
        double r17985 = 0.954929658551372;
        double r17986 = 0.12900613773279798;
        double r17987 = r17986 * r17984;
        double r17988 = r17987 * r17984;
        double r17989 = r17985 - r17988;
        double r17990 = r17984 * r17989;
        return r17990;
}

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. 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 associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))