Average Error: 12.8 → 0.4
Time: 27.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left|\left|w \cdot r\right|\right| \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \cdot \sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}\right) - 4.5\]
\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(\left|\left|w \cdot r\right|\right| \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \cdot \sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}\right) - 4.5
double f(double v, double w, double r) {
        double r39467 = 3.0;
        double r39468 = 2.0;
        double r39469 = r;
        double r39470 = r39469 * r39469;
        double r39471 = r39468 / r39470;
        double r39472 = r39467 + r39471;
        double r39473 = 0.125;
        double r39474 = v;
        double r39475 = r39468 * r39474;
        double r39476 = r39467 - r39475;
        double r39477 = r39473 * r39476;
        double r39478 = w;
        double r39479 = r39478 * r39478;
        double r39480 = r39479 * r39469;
        double r39481 = r39480 * r39469;
        double r39482 = r39477 * r39481;
        double r39483 = 1.0;
        double r39484 = r39483 - r39474;
        double r39485 = r39482 / r39484;
        double r39486 = r39472 - r39485;
        double r39487 = 4.5;
        double r39488 = r39486 - r39487;
        return r39488;
}
↓
double f(double v, double w, double r) {
        double r39489 = 3.0;
        double r39490 = 2.0;
        double r39491 = r;
        double r39492 = r39491 * r39491;
        double r39493 = r39490 / r39492;
        double r39494 = r39489 + r39493;
        double r39495 = w;
        double r39496 = r39495 * r39491;
        double r39497 = fabs(r39496);
        double r39498 = fabs(r39497);
        double r39499 = 0.125;
        double r39500 = v;
        double r39501 = r39490 * r39500;
        double r39502 = r39489 - r39501;
        double r39503 = r39499 * r39502;
        double r39504 = 1.0;
        double r39505 = r39504 - r39500;
        double r39506 = r39503 / r39505;
        double r39507 = r39498 * r39506;
        double r39508 = 2.0;
        double r39509 = pow(r39497, r39508);
        double r39510 = sqrt(r39509);
        double r39511 = r39507 * r39510;
        double r39512 = r39494 - r39511;
        double r39513 = 4.5;
        double r39514 = r39512 - r39513;
        return r39514;
}

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

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

  12. Applied sqrt-prod0.4

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

  13. Simplified0.4

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

  15. Applied associate-/r/0.4

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

  16. Applied sqrt-prod0.5

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

  17. Applied associate-*r*0.5

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

  18. Simplified0.4

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

  19. Final simplification0.4

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

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))