Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 14.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x) {
        double r20696 = 0.954929658551372;
        double r20697 = x;
        double r20698 = r20696 * r20697;
        double r20699 = 0.12900613773279798;
        double r20700 = r20697 * r20697;
        double r20701 = r20700 * r20697;
        double r20702 = r20699 * r20701;
        double r20703 = r20698 - r20702;
        return r20703;
}

↓

double f(double x) {
        double r20704 = 0.954929658551372;
        double r20705 = x;
        double r20706 = r20704 * r20705;
        double r20707 = 0.12900613773279798;
        double r20708 = r20707 * r20705;
        double r20709 = r20705 * r20708;
        double r20710 = r20705 * r20709;
        double r20711 = r20706 - r20710;
        return r20711;
}

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. Simplified 0.1

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

10. Applied unpow3 0.1

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

11. Applied unpow-prod-down 0.1

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

12. Applied associate-*r* 0.1

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

13. Simplified 0.1

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

14. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))