Average Error: 12.1 → 0.3
Time: 45.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \frac{w \cdot r}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{r}}\]
\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{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \frac{w \cdot r}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{r}}
double f(double v, double w, double r) {
        double r2602458 = 3.0;
        double r2602459 = 2.0;
        double r2602460 = r;
        double r2602461 = r2602460 * r2602460;
        double r2602462 = r2602459 / r2602461;
        double r2602463 = r2602458 + r2602462;
        double r2602464 = 0.125;
        double r2602465 = v;
        double r2602466 = r2602459 * r2602465;
        double r2602467 = r2602458 - r2602466;
        double r2602468 = r2602464 * r2602467;
        double r2602469 = w;
        double r2602470 = r2602469 * r2602469;
        double r2602471 = r2602470 * r2602460;
        double r2602472 = r2602471 * r2602460;
        double r2602473 = r2602468 * r2602472;
        double r2602474 = 1.0;
        double r2602475 = r2602474 - r2602465;
        double r2602476 = r2602473 / r2602475;
        double r2602477 = r2602463 - r2602476;
        double r2602478 = 4.5;
        double r2602479 = r2602477 - r2602478;
        return r2602479;
}
↓
double f(double v, double w, double r) {
        double r2602480 = 2.0;
        double r2602481 = r;
        double r2602482 = r2602481 * r2602481;
        double r2602483 = r2602480 / r2602482;
        double r2602484 = 3.0;
        double r2602485 = 4.5;
        double r2602486 = r2602484 - r2602485;
        double r2602487 = r2602483 + r2602486;
        double r2602488 = w;
        double r2602489 = r2602488 * r2602481;
        double r2602490 = 1.0;
        double r2602491 = v;
        double r2602492 = r2602490 - r2602491;
        double r2602493 = 0.125;
        double r2602494 = r2602491 * r2602480;
        double r2602495 = r2602484 - r2602494;
        double r2602496 = r2602493 * r2602495;
        double r2602497 = r2602492 / r2602496;
        double r2602498 = sqrt(r2602497);
        double r2602499 = r2602498 / r2602488;
        double r2602500 = r2602498 / r2602481;
        double r2602501 = r2602499 * r2602500;
        double r2602502 = r2602489 / r2602501;
        double r2602503 = r2602487 - r2602502;
        return r2602503;
}

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 12.1

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

  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-sqrt0.3

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

  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 div-inv0.3

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

  8. Applied associate-/l*0.4

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019143 
(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))