Average Error: 0.1 → 0.1
Time: 2.2s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982
double f(double x) {
        double r18193 = 0.954929658551372;
        double r18194 = x;
        double r18195 = r18193 * r18194;
        double r18196 = 0.12900613773279798;
        double r18197 = r18194 * r18194;
        double r18198 = r18197 * r18194;
        double r18199 = r18196 * r18198;
        double r18200 = r18195 - r18199;
        return r18200;
}
↓
double f(double x) {
        double r18201 = 0.954929658551372;
        double r18202 = x;
        double r18203 = r18201 * r18202;
        double r18204 = 3.0;
        double r18205 = pow(r18202, r18204);
        double r18206 = 0.12900613773279798;
        double r18207 = r18205 * r18206;
        double r18208 = r18203 - r18207;
        return r18208;
}

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

    \[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{0.129006137732797982 \cdot {x}^{3}}\]

  3. Simplified0.1

    \[\leadsto 0.95492965855137202 \cdot x - \color{blue}{{x}^{3} \cdot 0.129006137732797982}\]

  4. Final simplification0.1

    \[\leadsto 0.95492965855137202 \cdot x - {x}^{3} \cdot 0.129006137732797982\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))