Average Error: 12.8 → 0.4
Time: 25.8s
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 r39472 = 3.0;
        double r39473 = 2.0;
        double r39474 = r;
        double r39475 = r39474 * r39474;
        double r39476 = r39473 / r39475;
        double r39477 = r39472 + r39476;
        double r39478 = 0.125;
        double r39479 = v;
        double r39480 = r39473 * r39479;
        double r39481 = r39472 - r39480;
        double r39482 = r39478 * r39481;
        double r39483 = w;
        double r39484 = r39483 * r39483;
        double r39485 = r39484 * r39474;
        double r39486 = r39485 * r39474;
        double r39487 = r39482 * r39486;
        double r39488 = 1.0;
        double r39489 = r39488 - r39479;
        double r39490 = r39487 / r39489;
        double r39491 = r39477 - r39490;
        double r39492 = 4.5;
        double r39493 = r39491 - r39492;
        return r39493;
}
↓
double f(double v, double w, double r) {
        double r39494 = 3.0;
        double r39495 = 2.0;
        double r39496 = r;
        double r39497 = r39496 * r39496;
        double r39498 = r39495 / r39497;
        double r39499 = r39494 + r39498;
        double r39500 = w;
        double r39501 = r39500 * r39496;
        double r39502 = fabs(r39501);
        double r39503 = fabs(r39502);
        double r39504 = 0.125;
        double r39505 = v;
        double r39506 = r39495 * r39505;
        double r39507 = r39494 - r39506;
        double r39508 = r39504 * r39507;
        double r39509 = 1.0;
        double r39510 = r39509 - r39505;
        double r39511 = r39508 / r39510;
        double r39512 = r39503 * r39511;
        double r39513 = 2.0;
        double r39514 = pow(r39502, r39513);
        double r39515 = sqrt(r39514);
        double r39516 = r39512 * r39515;
        double r39517 = r39499 - r39516;
        double r39518 = 4.5;
        double r39519 = r39517 - r39518;
        return r39519;
}

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))