Average Error: 12.3 → 0.3
Time: 28.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} - \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}} \cdot \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}\right) + \left(3 - 4.5\right)\]
\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{2}{r \cdot r} - \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}} \cdot \frac{w \cdot r}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - v \cdot 2\right)}}}\right) + \left(3 - 4.5\right)
double f(double v, double w, double r) {
        double r1089628 = 3.0;
        double r1089629 = 2.0;
        double r1089630 = r;
        double r1089631 = r1089630 * r1089630;
        double r1089632 = r1089629 / r1089631;
        double r1089633 = r1089628 + r1089632;
        double r1089634 = 0.125;
        double r1089635 = v;
        double r1089636 = r1089629 * r1089635;
        double r1089637 = r1089628 - r1089636;
        double r1089638 = r1089634 * r1089637;
        double r1089639 = w;
        double r1089640 = r1089639 * r1089639;
        double r1089641 = r1089640 * r1089630;
        double r1089642 = r1089641 * r1089630;
        double r1089643 = r1089638 * r1089642;
        double r1089644 = 1.0;
        double r1089645 = r1089644 - r1089635;
        double r1089646 = r1089643 / r1089645;
        double r1089647 = r1089633 - r1089646;
        double r1089648 = 4.5;
        double r1089649 = r1089647 - r1089648;
        return r1089649;
}
↓
double f(double v, double w, double r) {
        double r1089650 = 2.0;
        double r1089651 = r;
        double r1089652 = r1089651 * r1089651;
        double r1089653 = r1089650 / r1089652;
        double r1089654 = w;
        double r1089655 = r1089654 * r1089651;
        double r1089656 = 1.0;
        double r1089657 = v;
        double r1089658 = r1089656 - r1089657;
        double r1089659 = 0.125;
        double r1089660 = 3.0;
        double r1089661 = r1089657 * r1089650;
        double r1089662 = r1089660 - r1089661;
        double r1089663 = r1089659 * r1089662;
        double r1089664 = r1089658 / r1089663;
        double r1089665 = sqrt(r1089664);
        double r1089666 = r1089655 / r1089665;
        double r1089667 = r1089666 * r1089666;
        double r1089668 = r1089653 - r1089667;
        double r1089669 = 4.5;
        double r1089670 = r1089660 - r1089669;
        double r1089671 = r1089668 + r1089670;
        return r1089671;
}

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 12.3

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

  2. Simplified6.3

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

  4. Applied associate-/l*0.3

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

  6. Applied associate-/r*0.3

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

  8. Applied add-sqr-sqrt0.3

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

  9. Applied times-frac0.3

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

  11. Applied div-inv0.3

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

  12. Applied associate-/l*0.4

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019139 
(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))