Average Error: 12.8 → 0.5
Time: 25.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \sqrt{0.125} \cdot \left(\sqrt{\frac{3 - 2 \cdot v}{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \left(\sqrt{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}} \cdot \left|\left|w \cdot r\right|\right|\right)\right)\right) - 4.5\]
\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) - \sqrt{0.125} \cdot \left(\sqrt{\frac{3 - 2 \cdot v}{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \left(\sqrt{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}} \cdot \left|\left|w \cdot r\right|\right|\right)\right)\right) - 4.5
double f(double v, double w, double r) {
        double r39547 = 3.0;
        double r39548 = 2.0;
        double r39549 = r;
        double r39550 = r39549 * r39549;
        double r39551 = r39548 / r39550;
        double r39552 = r39547 + r39551;
        double r39553 = 0.125;
        double r39554 = v;
        double r39555 = r39548 * r39554;
        double r39556 = r39547 - r39555;
        double r39557 = r39553 * r39556;
        double r39558 = w;
        double r39559 = r39558 * r39558;
        double r39560 = r39559 * r39549;
        double r39561 = r39560 * r39549;
        double r39562 = r39557 * r39561;
        double r39563 = 1.0;
        double r39564 = r39563 - r39554;
        double r39565 = r39562 / r39564;
        double r39566 = r39552 - r39565;
        double r39567 = 4.5;
        double r39568 = r39566 - r39567;
        return r39568;
}
↓
double f(double v, double w, double r) {
        double r39569 = 3.0;
        double r39570 = 2.0;
        double r39571 = r;
        double r39572 = r39571 * r39571;
        double r39573 = r39570 / r39572;
        double r39574 = r39569 + r39573;
        double r39575 = 0.125;
        double r39576 = sqrt(r39575);
        double r39577 = v;
        double r39578 = r39570 * r39577;
        double r39579 = r39569 - r39578;
        double r39580 = 1.0;
        double r39581 = r39580 - r39577;
        double r39582 = w;
        double r39583 = r39582 * r39571;
        double r39584 = fabs(r39583);
        double r39585 = 2.0;
        double r39586 = pow(r39584, r39585);
        double r39587 = r39581 / r39586;
        double r39588 = r39579 / r39587;
        double r39589 = sqrt(r39588);
        double r39590 = r39575 * r39579;
        double r39591 = r39590 / r39581;
        double r39592 = sqrt(r39591);
        double r39593 = fabs(r39584);
        double r39594 = r39592 * r39593;
        double r39595 = r39589 * r39594;
        double r39596 = r39576 * r39595;
        double r39597 = r39574 - r39596;
        double r39598 = 4.5;
        double r39599 = r39597 - r39598;
        return r39599;
}

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 12.8

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

  3. Applied add-sqr-sqrt12.8

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

  4. Simplified12.8

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

  5. Simplified6.8

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

  7. Applied add-sqr-sqrt6.8

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

  8. Simplified6.8

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

  9. Simplified0.5

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

  11. Applied associate-/r/0.4

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

  12. Applied sqrt-prod0.4

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

  13. Simplified0.4

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

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

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

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

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

  17. Applied times-frac0.4

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

  18. Applied times-frac0.5

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

  19. Applied sqrt-prod0.5

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

  20. Applied associate-*l*0.5

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

  21. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(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))