Average Error: 12.7 → 0.3
Time: 7.7s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{\frac{1 - v}{\left|w \cdot r\right|}}{{\left(\left|w \cdot r\right|\right)}^{1}}}\right) - 4.5\]
\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{\frac{1 - v}{\left|w \cdot r\right|}}{{\left(\left|w \cdot r\right|\right)}^{1}}}\right) - 4.5
double f(double v, double w, double r) {
        double r19535 = 3.0;
        double r19536 = 2.0;
        double r19537 = r;
        double r19538 = r19537 * r19537;
        double r19539 = r19536 / r19538;
        double r19540 = r19535 + r19539;
        double r19541 = 0.125;
        double r19542 = v;
        double r19543 = r19536 * r19542;
        double r19544 = r19535 - r19543;
        double r19545 = r19541 * r19544;
        double r19546 = w;
        double r19547 = r19546 * r19546;
        double r19548 = r19547 * r19537;
        double r19549 = r19548 * r19537;
        double r19550 = r19545 * r19549;
        double r19551 = 1.0;
        double r19552 = r19551 - r19542;
        double r19553 = r19550 / r19552;
        double r19554 = r19540 - r19553;
        double r19555 = 4.5;
        double r19556 = r19554 - r19555;
        return r19556;
}
↓
double f(double v, double w, double r) {
        double r19557 = 3.0;
        double r19558 = 2.0;
        double r19559 = r;
        double r19560 = r19559 * r19559;
        double r19561 = r19558 / r19560;
        double r19562 = r19557 + r19561;
        double r19563 = 0.125;
        double r19564 = v;
        double r19565 = r19558 * r19564;
        double r19566 = r19557 - r19565;
        double r19567 = r19563 * r19566;
        double r19568 = 1.0;
        double r19569 = r19568 - r19564;
        double r19570 = w;
        double r19571 = r19570 * r19559;
        double r19572 = fabs(r19571);
        double r19573 = r19569 / r19572;
        double r19574 = 1.0;
        double r19575 = pow(r19572, r19574);
        double r19576 = r19573 / r19575;
        double r19577 = r19567 / r19576;
        double r19578 = r19562 - r19577;
        double r19579 = 4.5;
        double r19580 = r19578 - r19579;
        return r19580;
}

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-sqrt12.8

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

  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. Simplified6.5

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left|w \cdot r\right| \cdot \color{blue}{\left|w \cdot r\right|}\right)}{1 - v}\right) - 4.5\]
  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-sqrt0.5

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

  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 associate-/r*0.5

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

  13. Simplified0.4

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

  15. Applied pow1/20.4

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

  16. Applied pow-pow0.3

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

  17. Simplified0.3

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

  18. Final simplification0.3

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

Reproduce

herbie shell --seed 2020083 
(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))