Average Error: 12.9 → 0.4
Time: 7.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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) - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r27453 = 3.0;
        double r27454 = 2.0;
        double r27455 = r;
        double r27456 = r27455 * r27455;
        double r27457 = r27454 / r27456;
        double r27458 = r27453 + r27457;
        double r27459 = 0.125;
        double r27460 = v;
        double r27461 = r27454 * r27460;
        double r27462 = r27453 - r27461;
        double r27463 = r27459 * r27462;
        double r27464 = w;
        double r27465 = r27464 * r27464;
        double r27466 = r27465 * r27455;
        double r27467 = r27466 * r27455;
        double r27468 = r27463 * r27467;
        double r27469 = 1.0;
        double r27470 = r27469 - r27460;
        double r27471 = r27468 / r27470;
        double r27472 = r27458 - r27471;
        double r27473 = 4.5;
        double r27474 = r27472 - r27473;
        return r27474;
}
↓
double f(double v, double w, double r) {
        double r27475 = 3.0;
        double r27476 = 2.0;
        double r27477 = r;
        double r27478 = r27477 * r27477;
        double r27479 = r27476 / r27478;
        double r27480 = r27475 + r27479;
        double r27481 = 1.0;
        double r27482 = cbrt(r27481);
        double r27483 = r27482 * r27482;
        double r27484 = 1.0;
        double r27485 = v;
        double r27486 = r27484 - r27485;
        double r27487 = 0.125;
        double r27488 = r27476 * r27485;
        double r27489 = r27475 - r27488;
        double r27490 = r27487 * r27489;
        double r27491 = r27486 / r27490;
        double r27492 = w;
        double r27493 = r27492 * r27477;
        double r27494 = fabs(r27493);
        double r27495 = 2.0;
        double r27496 = pow(r27494, r27495);
        double r27497 = r27491 / r27496;
        double r27498 = sqrt(r27497);
        double r27499 = r27483 / r27498;
        double r27500 = r27482 / r27498;
        double r27501 = r27499 * r27500;
        double r27502 = r27480 - r27501;
        double r27503 = 4.5;
        double r27504 = r27502 - r27503;
        return r27504;
}

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 12.9

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

  3. Applied add-sqr-sqrt13.0

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

  4. Simplified12.9

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

  5. Simplified6.6

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

  7. Applied clear-num6.7

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

  8. Simplified0.4

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

  10. Applied add-sqr-sqrt0.4

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

  11. Applied add-cube-cbrt0.4

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

  12. Applied times-frac0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2020064 
(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))