Average Error: 12.6 → 0.3
Time: 5.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left|w \cdot r\right|\right) \cdot \frac{3 - 2 \cdot v}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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
↓
\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left|w \cdot r\right|\right) \cdot \frac{3 - 2 \cdot v}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r17505 = 3.0;
        double r17506 = 2.0;
        double r17507 = r;
        double r17508 = r17507 * r17507;
        double r17509 = r17506 / r17508;
        double r17510 = r17505 + r17509;
        double r17511 = 0.125;
        double r17512 = v;
        double r17513 = r17506 * r17512;
        double r17514 = r17505 - r17513;
        double r17515 = r17511 * r17514;
        double r17516 = w;
        double r17517 = r17516 * r17516;
        double r17518 = r17517 * r17507;
        double r17519 = r17518 * r17507;
        double r17520 = r17515 * r17519;
        double r17521 = 1.0;
        double r17522 = r17521 - r17512;
        double r17523 = r17520 / r17522;
        double r17524 = r17510 - r17523;
        double r17525 = 4.5;
        double r17526 = r17524 - r17525;
        return r17526;
}
↓
double f(double v, double w, double r) {
        double r17527 = 3.0;
        double r17528 = 2.0;
        double r17529 = r;
        double r17530 = r17528 / r17529;
        double r17531 = r17530 / r17529;
        double r17532 = r17527 + r17531;
        double r17533 = 0.125;
        double r17534 = w;
        double r17535 = r17534 * r17529;
        double r17536 = fabs(r17535);
        double r17537 = r17533 * r17536;
        double r17538 = v;
        double r17539 = r17528 * r17538;
        double r17540 = r17527 - r17539;
        double r17541 = 1.0;
        double r17542 = r17541 - r17538;
        double r17543 = r17542 / r17536;
        double r17544 = r17540 / r17543;
        double r17545 = r17537 * r17544;
        double r17546 = r17532 - r17545;
        double r17547 = 4.5;
        double r17548 = r17546 - r17547;
        return r17548;
}

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 12.6

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.6

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

  5. Simplified6.4

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

  7. Applied associate-/l*0.4

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

  8. Simplified0.4

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

  10. Applied associate-/r*0.4

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

  12. Applied add-sqr-sqrt0.5

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

  13. Applied unpow-prod-down0.5

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

  14. Applied *-un-lft-identity0.5

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

  15. Applied times-frac0.5

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

  16. Applied times-frac0.5

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

  17. Simplified0.4

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

  18. Simplified0.3

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

  19. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))