Average Error: 12.7 → 0.4
Time: 6.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1}{\left|w \cdot r\right|} \cdot \frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1}{\left|w \cdot r\right|} \cdot \frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r15377 = 3.0;
        double r15378 = 2.0;
        double r15379 = r;
        double r15380 = r15379 * r15379;
        double r15381 = r15378 / r15380;
        double r15382 = r15377 + r15381;
        double r15383 = 0.125;
        double r15384 = v;
        double r15385 = r15378 * r15384;
        double r15386 = r15377 - r15385;
        double r15387 = r15383 * r15386;
        double r15388 = w;
        double r15389 = r15388 * r15388;
        double r15390 = r15389 * r15379;
        double r15391 = r15390 * r15379;
        double r15392 = r15387 * r15391;
        double r15393 = 1.0;
        double r15394 = r15393 - r15384;
        double r15395 = r15392 / r15394;
        double r15396 = r15382 - r15395;
        double r15397 = 4.5;
        double r15398 = r15396 - r15397;
        return r15398;
}
↓
double f(double v, double w, double r) {
        double r15399 = 3.0;
        double r15400 = 2.0;
        double r15401 = r;
        double r15402 = r15401 * r15401;
        double r15403 = r15400 / r15402;
        double r15404 = r15399 + r15403;
        double r15405 = 0.125;
        double r15406 = v;
        double r15407 = r15400 * r15406;
        double r15408 = r15399 - r15407;
        double r15409 = r15405 * r15408;
        double r15410 = 1.0;
        double r15411 = w;
        double r15412 = r15411 * r15401;
        double r15413 = fabs(r15412);
        double r15414 = r15410 / r15413;
        double r15415 = 1.0;
        double r15416 = r15415 - r15406;
        double r15417 = r15416 / r15413;
        double r15418 = r15414 * r15417;
        double r15419 = r15409 / r15418;
        double r15420 = r15404 - r15419;
        double r15421 = 4.5;
        double r15422 = r15420 - r15421;
        return r15422;
}

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 12.7

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.7

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

  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 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-sqrt0.5

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

  11. Applied unpow-prod-down0.5

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

  12. Applied *-un-lft-identity0.5

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019353 
(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))