Average Error: 12.2 → 0.3
Time: 45.8s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}} \cdot \left(\frac{1}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{r}\right)}\]
\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{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}} \cdot \left(\frac{1}{w} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}{r}\right)}
double f(double v, double w, double r) {
        double r2588478 = 3.0;
        double r2588479 = 2.0;
        double r2588480 = r;
        double r2588481 = r2588480 * r2588480;
        double r2588482 = r2588479 / r2588481;
        double r2588483 = r2588478 + r2588482;
        double r2588484 = 0.125;
        double r2588485 = v;
        double r2588486 = r2588479 * r2588485;
        double r2588487 = r2588478 - r2588486;
        double r2588488 = r2588484 * r2588487;
        double r2588489 = w;
        double r2588490 = r2588489 * r2588489;
        double r2588491 = r2588490 * r2588480;
        double r2588492 = r2588491 * r2588480;
        double r2588493 = r2588488 * r2588492;
        double r2588494 = 1.0;
        double r2588495 = r2588494 - r2588485;
        double r2588496 = r2588493 / r2588495;
        double r2588497 = r2588483 - r2588496;
        double r2588498 = 4.5;
        double r2588499 = r2588497 - r2588498;
        return r2588499;
}
↓
double f(double v, double w, double r) {
        double r2588500 = 2.0;
        double r2588501 = r;
        double r2588502 = r2588500 / r2588501;
        double r2588503 = r2588502 / r2588501;
        double r2588504 = 3.0;
        double r2588505 = 4.5;
        double r2588506 = r2588504 - r2588505;
        double r2588507 = r2588503 + r2588506;
        double r2588508 = w;
        double r2588509 = r2588508 * r2588501;
        double r2588510 = 1.0;
        double r2588511 = v;
        double r2588512 = r2588510 - r2588511;
        double r2588513 = 0.125;
        double r2588514 = r2588511 * r2588500;
        double r2588515 = r2588504 - r2588514;
        double r2588516 = r2588513 * r2588515;
        double r2588517 = r2588512 / r2588516;
        double r2588518 = sqrt(r2588517);
        double r2588519 = r2588510 / r2588508;
        double r2588520 = r2588518 / r2588501;
        double r2588521 = r2588519 * r2588520;
        double r2588522 = r2588518 * r2588521;
        double r2588523 = r2588509 / r2588522;
        double r2588524 = r2588507 - r2588523;
        return r2588524;
}

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 12.2

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

  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 div-inv0.3

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

  8. Applied associate-*l*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019144 
(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))