Average Error: 12.2 → 0.4
Time: 6.2s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{1}{\frac{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \frac{1}{\frac{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r19428 = 3.0;
        double r19429 = 2.0;
        double r19430 = r;
        double r19431 = r19430 * r19430;
        double r19432 = r19429 / r19431;
        double r19433 = r19428 + r19432;
        double r19434 = 0.125;
        double r19435 = v;
        double r19436 = r19429 * r19435;
        double r19437 = r19428 - r19436;
        double r19438 = r19434 * r19437;
        double r19439 = w;
        double r19440 = r19439 * r19439;
        double r19441 = r19440 * r19430;
        double r19442 = r19441 * r19430;
        double r19443 = r19438 * r19442;
        double r19444 = 1.0;
        double r19445 = r19444 - r19435;
        double r19446 = r19443 / r19445;
        double r19447 = r19433 - r19446;
        double r19448 = 4.5;
        double r19449 = r19447 - r19448;
        return r19449;
}
↓
double f(double v, double w, double r) {
        double r19450 = 3.0;
        double r19451 = 2.0;
        double r19452 = r;
        double r19453 = r19451 / r19452;
        double r19454 = r19453 / r19452;
        double r19455 = r19450 + r19454;
        double r19456 = 1.0;
        double r19457 = 1.0;
        double r19458 = v;
        double r19459 = r19457 - r19458;
        double r19460 = 0.125;
        double r19461 = r19451 * r19458;
        double r19462 = r19450 - r19461;
        double r19463 = r19460 * r19462;
        double r19464 = r19459 / r19463;
        double r19465 = w;
        double r19466 = r19465 * r19452;
        double r19467 = fabs(r19466);
        double r19468 = 2.0;
        double r19469 = pow(r19467, r19468);
        double r19470 = sqrt(r19469);
        double r19471 = r19464 / r19470;
        double r19472 = r19471 / r19470;
        double r19473 = r19456 / r19472;
        double r19474 = r19455 - r19473;
        double r19475 = 4.5;
        double r19476 = r19474 - r19475;
        return r19476;
}

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 12.2

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

  3. Applied add-sqr-sqrt12.2

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

  4. Simplified12.2

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

  5. Simplified6.2

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

  7. Applied clear-num6.2

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

  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

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

  11. Applied associate-/r*0.4

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

  13. Applied associate-/r*0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(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))