Rosa's TurbineBenchmark

Average Error: 13.0 → 0.4

Time: 12.5s

Precision: 64

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

Math

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]

↓

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)\right) - 4.5\]

C

double f(double v, double w, double r) {
        double r15551 = 3.0;
        double r15552 = 2.0;
        double r15553 = r;
        double r15554 = r15553 * r15553;
        double r15555 = r15552 / r15554;
        double r15556 = r15551 + r15555;
        double r15557 = 0.125;
        double r15558 = v;
        double r15559 = r15552 * r15558;
        double r15560 = r15551 - r15559;
        double r15561 = r15557 * r15560;
        double r15562 = w;
        double r15563 = r15562 * r15562;
        double r15564 = r15563 * r15553;
        double r15565 = r15564 * r15553;
        double r15566 = r15561 * r15565;
        double r15567 = 1.0;
        double r15568 = r15567 - r15558;
        double r15569 = r15566 / r15568;
        double r15570 = r15556 - r15569;
        double r15571 = 4.5;
        double r15572 = r15570 - r15571;
        return r15572;
}

↓

double f(double v, double w, double r) {
        double r15573 = 3.0;
        double r15574 = 2.0;
        double r15575 = r;
        double r15576 = r15575 * r15575;
        double r15577 = r15574 / r15576;
        double r15578 = r15573 + r15577;
        double r15579 = w;
        double r15580 = r15579 * r15575;
        double r15581 = r15580 * r15580;
        double r15582 = 1.0;
        double r15583 = v;
        double r15584 = r15582 - r15583;
        double r15585 = r15581 / r15584;
        double r15586 = 0.125;
        double r15587 = r15574 * r15583;
        double r15588 = r15573 - r15587;
        double r15589 = r15586 * r15588;
        double r15590 = r15585 * r15589;
        double r15591 = r15578 - r15590;
        double r15592 = 4.5;
        double r15593 = r15591 - r15592;
        return r15593;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Derivation

1. Initial program 13.0

   \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
2. Using strategy rm

3. Applied associate-*l* 8.2

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\color{blue}{\left(w \cdot \left(w \cdot r\right)\right)} \cdot r\right)}{1 - v}\right) - 4.5\]
4. Using strategy rm

5. Applied *-un-lft-identity 8.2

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 4.5\]

6. Applied times-frac 2.5

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1} \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}}\right) - 4.5\]

7. Simplified 2.5

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\]
8. Using strategy rm

9. Applied pow1 2.5

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot \color{blue}{{r}^{1}}}{1 - v}\right) - 4.5\]

10. Applied pow1 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot \color{blue}{{r}^{1}}\right)\right) \cdot {r}^{1}}{1 - v}\right) - 4.5\]

11. Applied pow1 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(\color{blue}{{w}^{1}} \cdot {r}^{1}\right)\right) \cdot {r}^{1}}{1 - v}\right) - 4.5\]

12. Applied pow-prod-down 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \color{blue}{{\left(w \cdot r\right)}^{1}}\right) \cdot {r}^{1}}{1 - v}\right) - 4.5\]

13. Applied pow1 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(\color{blue}{{w}^{1}} \cdot {\left(w \cdot r\right)}^{1}\right) \cdot {r}^{1}}{1 - v}\right) - 4.5\]

14. Applied pow-prod-down 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{{\left(w \cdot \left(w \cdot r\right)\right)}^{1}} \cdot {r}^{1}}{1 - v}\right) - 4.5\]

15. Applied pow-prod-down 2.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{{\left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)}^{1}}}{1 - v}\right) - 4.5\]

16. Simplified 0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\color{blue}{\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)}}^{1}}{1 - v}\right) - 4.5\]

17. Final simplification 0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)\right) - 4.5\]

Reproduce

herbie shell --seed 2020043 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))