Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 9.7s

Precision: 64

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

Math

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

↓

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

C

double f(double x) {
        double r26701 = 0.954929658551372;
        double r26702 = x;
        double r26703 = r26701 * r26702;
        double r26704 = 0.12900613773279798;
        double r26705 = r26702 * r26702;
        double r26706 = r26705 * r26702;
        double r26707 = r26704 * r26706;
        double r26708 = r26703 - r26707;
        return r26708;
}

↓

double f(double x) {
        double r26709 = 0.954929658551372;
        double r26710 = x;
        double r26711 = r26709 * r26710;
        double r26712 = 0.12900613773279798;
        double r26713 = 3.0;
        double r26714 = pow(r26710, r26713);
        double r26715 = r26712 * r26714;
        double r26716 = r26711 - r26715;
        return r26716;
}

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. Final simplification 0.1

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

Reproduce

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