Average Error: 12.7 → 0.4
Time: 5.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \sqrt{\left|w \cdot r\right|}\right) \cdot \frac{3 - 2 \cdot v}{\frac{\frac{1 - v}{\left|w \cdot r\right|}}{\sqrt{\left|w \cdot r\right|}}}\right) - 4.5\]
\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{2}{r \cdot r}\right) - \left(0.125 \cdot \sqrt{\left|w \cdot r\right|}\right) \cdot \frac{3 - 2 \cdot v}{\frac{\frac{1 - v}{\left|w \cdot r\right|}}{\sqrt{\left|w \cdot r\right|}}}\right) - 4.5
double f(double v, double w, double r) {
        double r16559 = 3.0;
        double r16560 = 2.0;
        double r16561 = r;
        double r16562 = r16561 * r16561;
        double r16563 = r16560 / r16562;
        double r16564 = r16559 + r16563;
        double r16565 = 0.125;
        double r16566 = v;
        double r16567 = r16560 * r16566;
        double r16568 = r16559 - r16567;
        double r16569 = r16565 * r16568;
        double r16570 = w;
        double r16571 = r16570 * r16570;
        double r16572 = r16571 * r16561;
        double r16573 = r16572 * r16561;
        double r16574 = r16569 * r16573;
        double r16575 = 1.0;
        double r16576 = r16575 - r16566;
        double r16577 = r16574 / r16576;
        double r16578 = r16564 - r16577;
        double r16579 = 4.5;
        double r16580 = r16578 - r16579;
        return r16580;
}
↓
double f(double v, double w, double r) {
        double r16581 = 3.0;
        double r16582 = 2.0;
        double r16583 = r;
        double r16584 = r16583 * r16583;
        double r16585 = r16582 / r16584;
        double r16586 = r16581 + r16585;
        double r16587 = 0.125;
        double r16588 = w;
        double r16589 = r16588 * r16583;
        double r16590 = fabs(r16589);
        double r16591 = sqrt(r16590);
        double r16592 = r16587 * r16591;
        double r16593 = v;
        double r16594 = r16582 * r16593;
        double r16595 = r16581 - r16594;
        double r16596 = 1.0;
        double r16597 = r16596 - r16593;
        double r16598 = r16597 / r16590;
        double r16599 = r16598 / r16591;
        double r16600 = r16595 / r16599;
        double r16601 = r16592 * r16600;
        double r16602 = r16586 - r16601;
        double r16603 = 4.5;
        double r16604 = r16602 - r16603;
        return r16604;
}

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 12.7

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

  3. Applied associate-/l*8.6

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

  5. Applied add-sqr-sqrt8.6

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

  6. Simplified8.6

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

  7. Simplified0.4

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

  9. Applied associate-/r*0.3

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

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

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

  12. Applied add-sqr-sqrt0.4

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

  13. Applied *-un-lft-identity0.4

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

  14. Applied times-frac0.4

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

  15. Applied times-frac0.4

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

  16. Applied times-frac0.4

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

  17. Simplified0.4

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

  18. Simplified0.4

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

  19. Final simplification0.4

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

Reproduce

herbie shell --seed 2020060 
(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))