Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 1.9s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r13820 = 0.954929658551372;
        double r13821 = x;
        double r13822 = r13820 * r13821;
        double r13823 = 0.12900613773279798;
        double r13824 = r13821 * r13821;
        double r13825 = r13824 * r13821;
        double r13826 = r13823 * r13825;
        double r13827 = r13822 - r13826;
        return r13827;
}

↓

double f(double x) {
        double r13828 = 0.954929658551372;
        double r13829 = x;
        double r13830 = r13828 * r13829;
        double r13831 = 0.12900613773279798;
        double r13832 = r13829 * r13831;
        double r13833 = r13829 * r13832;
        double r13834 = r13829 * r13833;
        double r13835 = 1.0;
        double r13836 = pow(r13834, r13835);
        double r13837 = r13830 - r13836;
        return r13837;
}

Error

Bits error versus x

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 pow1 0.1

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

4. Applied pow1 0.1

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

5. Applied pow1 0.1

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

6. Applied pow-prod-down 0.1

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

7. Applied pow-prod-down 0.1

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

8. Applied pow1 0.1

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

9. Applied pow-prod-down 0.1

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

10. Simplified 0.1

    \[\leadsto 0.95492965855137202 \cdot x - {\color{blue}{\left({x}^{3} \cdot 0.129006137732797982\right)}}^{1}\]
11. Using strategy rm

12. Applied unpow3 0.1

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

13. Applied associate-*l* 0.1

    \[\leadsto 0.95492965855137202 \cdot x - {\color{blue}{\left(\left(x \cdot x\right) \cdot \left(x \cdot 0.129006137732797982\right)\right)}}^{1}\]
14. Using strategy rm

15. Applied associate-*l* 0.1

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

16. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))