Average Error: 11.8 → 0.7
Time: 38.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\frac{2}{r}}\right) \cdot \sqrt[3]{\frac{\sqrt{2}}{r}}}{\frac{r}{\sqrt[3]{\frac{2}{r}}}} + \left(3 - 4.5\right)\right) - \frac{r \cdot w}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{r}}\]
\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(\frac{\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\frac{2}{r}}\right) \cdot \sqrt[3]{\frac{\sqrt{2}}{r}}}{\frac{r}{\sqrt[3]{\frac{2}{r}}}} + \left(3 - 4.5\right)\right) - \frac{r \cdot w}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{r}}
double f(double v, double w, double r) {
        double r1803438 = 3.0;
        double r1803439 = 2.0;
        double r1803440 = r;
        double r1803441 = r1803440 * r1803440;
        double r1803442 = r1803439 / r1803441;
        double r1803443 = r1803438 + r1803442;
        double r1803444 = 0.125;
        double r1803445 = v;
        double r1803446 = r1803439 * r1803445;
        double r1803447 = r1803438 - r1803446;
        double r1803448 = r1803444 * r1803447;
        double r1803449 = w;
        double r1803450 = r1803449 * r1803449;
        double r1803451 = r1803450 * r1803440;
        double r1803452 = r1803451 * r1803440;
        double r1803453 = r1803448 * r1803452;
        double r1803454 = 1.0;
        double r1803455 = r1803454 - r1803445;
        double r1803456 = r1803453 / r1803455;
        double r1803457 = r1803443 - r1803456;
        double r1803458 = 4.5;
        double r1803459 = r1803457 - r1803458;
        return r1803459;
}
↓
double f(double v, double w, double r) {
        double r1803460 = 2.0;
        double r1803461 = sqrt(r1803460);
        double r1803462 = cbrt(r1803461);
        double r1803463 = r;
        double r1803464 = r1803460 / r1803463;
        double r1803465 = cbrt(r1803464);
        double r1803466 = r1803462 * r1803465;
        double r1803467 = r1803461 / r1803463;
        double r1803468 = cbrt(r1803467);
        double r1803469 = r1803466 * r1803468;
        double r1803470 = r1803463 / r1803465;
        double r1803471 = r1803469 / r1803470;
        double r1803472 = 3.0;
        double r1803473 = 4.5;
        double r1803474 = r1803472 - r1803473;
        double r1803475 = r1803471 + r1803474;
        double r1803476 = w;
        double r1803477 = r1803463 * r1803476;
        double r1803478 = 1.0;
        double r1803479 = v;
        double r1803480 = r1803478 - r1803479;
        double r1803481 = 0.125;
        double r1803482 = r1803460 * r1803479;
        double r1803483 = r1803472 - r1803482;
        double r1803484 = r1803481 * r1803483;
        double r1803485 = r1803480 / r1803484;
        double r1803486 = sqrt(r1803485);
        double r1803487 = r1803486 / r1803476;
        double r1803488 = r1803486 / r1803463;
        double r1803489 = r1803487 * r1803488;
        double r1803490 = r1803477 / r1803489;
        double r1803491 = r1803475 - r1803490;
        return r1803491;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 11.8

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

  2. Simplified0.3

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

  4. Applied add-sqr-sqrt0.4

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

  5. Applied times-frac0.3

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

  7. Applied add-cube-cbrt0.7

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

  8. Applied associate-/l*0.7

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

  10. Applied *-un-lft-identity0.7

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

  11. Applied add-sqr-sqrt0.7

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

  12. Applied times-frac0.7

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

  13. Applied cbrt-prod0.7

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

  14. Applied associate-*r*0.7

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

  15. Simplified0.7

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

  16. Final simplification0.7

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

Reproduce

herbie shell --seed 2019146 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))