Average Error: 12.5 → 0.6
Time: 30.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\frac{\left(3 - v \cdot 2\right) \cdot 0.125}{\sqrt[3]{1 - v}} \cdot \sqrt{\sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}}\right) \cdot \sqrt{\sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}}\right) \cdot \sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}\]
\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{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\frac{\left(3 - v \cdot 2\right) \cdot 0.125}{\sqrt[3]{1 - v}} \cdot \sqrt{\sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}}\right) \cdot \sqrt{\sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}}\right) \cdot \sqrt{\frac{\frac{w \cdot r}{\sqrt[3]{1 - v}} \cdot \left(w \cdot r\right)}{\sqrt[3]{1 - v}}}
double f(double v, double w, double r) {
        double r933449 = 3.0;
        double r933450 = 2.0;
        double r933451 = r;
        double r933452 = r933451 * r933451;
        double r933453 = r933450 / r933452;
        double r933454 = r933449 + r933453;
        double r933455 = 0.125;
        double r933456 = v;
        double r933457 = r933450 * r933456;
        double r933458 = r933449 - r933457;
        double r933459 = r933455 * r933458;
        double r933460 = w;
        double r933461 = r933460 * r933460;
        double r933462 = r933461 * r933451;
        double r933463 = r933462 * r933451;
        double r933464 = r933459 * r933463;
        double r933465 = 1.0;
        double r933466 = r933465 - r933456;
        double r933467 = r933464 / r933466;
        double r933468 = r933454 - r933467;
        double r933469 = 4.5;
        double r933470 = r933468 - r933469;
        return r933470;
}
↓
double f(double v, double w, double r) {
        double r933471 = 2.0;
        double r933472 = r;
        double r933473 = r933472 * r933472;
        double r933474 = r933471 / r933473;
        double r933475 = 3.0;
        double r933476 = 4.5;
        double r933477 = r933475 - r933476;
        double r933478 = r933474 + r933477;
        double r933479 = v;
        double r933480 = r933479 * r933471;
        double r933481 = r933475 - r933480;
        double r933482 = 0.125;
        double r933483 = r933481 * r933482;
        double r933484 = 1.0;
        double r933485 = r933484 - r933479;
        double r933486 = cbrt(r933485);
        double r933487 = r933483 / r933486;
        double r933488 = w;
        double r933489 = r933488 * r933472;
        double r933490 = r933489 / r933486;
        double r933491 = r933490 * r933489;
        double r933492 = r933491 / r933486;
        double r933493 = sqrt(r933492);
        double r933494 = sqrt(r933493);
        double r933495 = r933487 * r933494;
        double r933496 = r933495 * r933494;
        double r933497 = r933496 * r933493;
        double r933498 = r933478 - r933497;
        return r933498;
}

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 12.5

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

  2. Simplified6.5

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

  4. Applied add-cube-cbrt6.6

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

  5. Applied times-frac0.5

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

  6. Simplified0.5

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

  8. Applied associate-*r/0.5

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

  10. Applied add-sqr-sqrt0.5

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

  11. Applied associate-*l*0.5

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

  13. Applied add-sqr-sqrt0.5

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

  14. Applied sqrt-prod0.6

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

  15. Applied associate-*l*0.6

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

  16. Final simplification0.6

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

Reproduce

herbie shell --seed 2019152 
(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))