Average Error: 0.1 → 0.1
Time: 2.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}
double f(double x) {
        double r18834 = 0.954929658551372;
        double r18835 = x;
        double r18836 = r18834 * r18835;
        double r18837 = 0.12900613773279798;
        double r18838 = r18835 * r18835;
        double r18839 = r18838 * r18835;
        double r18840 = r18837 * r18839;
        double r18841 = r18836 - r18840;
        return r18841;
}
↓
double f(double x) {
        double r18842 = 0.954929658551372;
        double r18843 = x;
        double r18844 = r18842 * r18843;
        double r18845 = 0.12900613773279798;
        double r18846 = 3.0;
        double r18847 = pow(r18843, r18846);
        double r18848 = r18845 * r18847;
        double r18849 = r18844 - r18848;
        return r18849;
}

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. Using strategy rm

  3. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot \color{blue}{{x}^{1}}\right)\]

  4. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot \color{blue}{{x}^{1}}\right) \cdot {x}^{1}\right)\]

  5. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(\color{blue}{{x}^{1}} \cdot {x}^{1}\right) \cdot {x}^{1}\right)\]

  6. Applied pow-prod-up0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\color{blue}{{x}^{\left(1 + 1\right)}} \cdot {x}^{1}\right)\]

  7. Applied pow-prod-up0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \color{blue}{{x}^{\left(\left(1 + 1\right) + 1\right)}}\]

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))