Average Error: 12.9 → 0.4
Time: 20.7s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{1}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{\left(3 - 2 \cdot v\right) \cdot 0.125}}\right) - 4.5\]
\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{1}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{\left(3 - 2 \cdot v\right) \cdot 0.125}}\right) - 4.5
double f(double v, double w, double r) {
        double r24344 = 3.0;
        double r24345 = 2.0;
        double r24346 = r;
        double r24347 = r24346 * r24346;
        double r24348 = r24345 / r24347;
        double r24349 = r24344 + r24348;
        double r24350 = 0.125;
        double r24351 = v;
        double r24352 = r24345 * r24351;
        double r24353 = r24344 - r24352;
        double r24354 = r24350 * r24353;
        double r24355 = w;
        double r24356 = r24355 * r24355;
        double r24357 = r24356 * r24346;
        double r24358 = r24357 * r24346;
        double r24359 = r24354 * r24358;
        double r24360 = 1.0;
        double r24361 = r24360 - r24351;
        double r24362 = r24359 / r24361;
        double r24363 = r24349 - r24362;
        double r24364 = 4.5;
        double r24365 = r24363 - r24364;
        return r24365;
}
↓
double f(double v, double w, double r) {
        double r24366 = 3.0;
        double r24367 = 2.0;
        double r24368 = r;
        double r24369 = r24368 * r24368;
        double r24370 = r24367 / r24369;
        double r24371 = r24366 + r24370;
        double r24372 = 1.0;
        double r24373 = 1.0;
        double r24374 = v;
        double r24375 = r24373 - r24374;
        double r24376 = w;
        double r24377 = r24376 * r24368;
        double r24378 = fabs(r24377);
        double r24379 = 2.0;
        double r24380 = pow(r24378, r24379);
        double r24381 = r24375 / r24380;
        double r24382 = r24367 * r24374;
        double r24383 = r24366 - r24382;
        double r24384 = 0.125;
        double r24385 = r24383 * r24384;
        double r24386 = r24381 / r24385;
        double r24387 = r24372 / r24386;
        double r24388 = r24371 - r24387;
        double r24389 = 4.5;
        double r24390 = r24388 - r24389;
        return r24390;
}

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-sqrt12.9

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

  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. Simplified6.5

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

  7. Applied associate-/l*0.4

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

  8. Simplified0.4

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

  10. Applied add-sqr-sqrt0.6

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

  11. Applied unpow-prod-down0.6

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

  12. Applied *-un-lft-identity0.6

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

  13. Applied times-frac0.5

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

  14. Simplified0.4

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

  15. Simplified0.4

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

  17. Applied clear-num0.4

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

  18. Simplified0.4

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

  19. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(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))