Average Error: 13.3 → 0.4
Time: 5.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1}{\left|w \cdot r\right|} \cdot \frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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{\frac{2}{r}}{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 r17525 = 3.0;
        double r17526 = 2.0;
        double r17527 = r;
        double r17528 = r17527 * r17527;
        double r17529 = r17526 / r17528;
        double r17530 = r17525 + r17529;
        double r17531 = 0.125;
        double r17532 = v;
        double r17533 = r17526 * r17532;
        double r17534 = r17525 - r17533;
        double r17535 = r17531 * r17534;
        double r17536 = w;
        double r17537 = r17536 * r17536;
        double r17538 = r17537 * r17527;
        double r17539 = r17538 * r17527;
        double r17540 = r17535 * r17539;
        double r17541 = 1.0;
        double r17542 = r17541 - r17532;
        double r17543 = r17540 / r17542;
        double r17544 = r17530 - r17543;
        double r17545 = 4.5;
        double r17546 = r17544 - r17545;
        return r17546;
}
↓
double f(double v, double w, double r) {
        double r17547 = 3.0;
        double r17548 = 2.0;
        double r17549 = r;
        double r17550 = r17548 / r17549;
        double r17551 = r17550 / r17549;
        double r17552 = r17547 + r17551;
        double r17553 = 0.125;
        double r17554 = v;
        double r17555 = r17548 * r17554;
        double r17556 = r17547 - r17555;
        double r17557 = r17553 * r17556;
        double r17558 = 1.0;
        double r17559 = w;
        double r17560 = r17559 * r17549;
        double r17561 = fabs(r17560);
        double r17562 = r17558 / r17561;
        double r17563 = 1.0;
        double r17564 = r17563 - r17554;
        double r17565 = r17564 / r17561;
        double r17566 = r17562 * r17565;
        double r17567 = r17557 / r17566;
        double r17568 = r17552 - r17567;
        double r17569 = 4.5;
        double r17570 = r17568 - r17569;
        return r17570;
}

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 13.3

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

  3. Applied add-sqr-sqrt13.3

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

  4. Simplified13.3

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

  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 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 associate-/r*0.5

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

  12. Applied add-sqr-sqrt0.6

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

  13. Applied unpow-prod-down0.6

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

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

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

  15. Applied times-frac0.5

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

  16. Simplified0.5

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

  17. Simplified0.4

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

  18. Final simplification0.4

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

Reproduce

herbie shell --seed 2020018 
(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))