Average Error: 12.1 → 0.3
Time: 21.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \frac{w \cdot r}{\frac{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}{r} \cdot \frac{1}{w}}\]
\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}{\frac{\frac{1 - v}{\left(3 - v \cdot 2\right) \cdot 0.125}}{r} \cdot \frac{1}{w}}
double f(double v, double w, double r) {
        double r889499 = 3.0;
        double r889500 = 2.0;
        double r889501 = r;
        double r889502 = r889501 * r889501;
        double r889503 = r889500 / r889502;
        double r889504 = r889499 + r889503;
        double r889505 = 0.125;
        double r889506 = v;
        double r889507 = r889500 * r889506;
        double r889508 = r889499 - r889507;
        double r889509 = r889505 * r889508;
        double r889510 = w;
        double r889511 = r889510 * r889510;
        double r889512 = r889511 * r889501;
        double r889513 = r889512 * r889501;
        double r889514 = r889509 * r889513;
        double r889515 = 1.0;
        double r889516 = r889515 - r889506;
        double r889517 = r889514 / r889516;
        double r889518 = r889504 - r889517;
        double r889519 = 4.5;
        double r889520 = r889518 - r889519;
        return r889520;
}
↓
double f(double v, double w, double r) {
        double r889521 = 2.0;
        double r889522 = r;
        double r889523 = r889521 / r889522;
        double r889524 = r889523 / r889522;
        double r889525 = 3.0;
        double r889526 = 4.5;
        double r889527 = r889525 - r889526;
        double r889528 = r889524 + r889527;
        double r889529 = w;
        double r889530 = r889529 * r889522;
        double r889531 = 1.0;
        double r889532 = v;
        double r889533 = r889531 - r889532;
        double r889534 = r889532 * r889521;
        double r889535 = r889525 - r889534;
        double r889536 = 0.125;
        double r889537 = r889535 * r889536;
        double r889538 = r889533 / r889537;
        double r889539 = r889538 / r889522;
        double r889540 = r889531 / r889529;
        double r889541 = r889539 * r889540;
        double r889542 = r889530 / r889541;
        double r889543 = r889528 - r889542;
        return r889543;
}

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. Simplified6.3

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

  4. Applied associate-/l*0.4

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

  6. Applied associate-/r*0.4

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

  8. Applied associate-/l*0.3

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

  10. Applied *-un-lft-identity0.3

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

  11. Applied times-frac0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019154 
(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))