Average Error: 12.9 → 0.3
Time: 5.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r15578 = 3.0;
        double r15579 = 2.0;
        double r15580 = r;
        double r15581 = r15580 * r15580;
        double r15582 = r15579 / r15581;
        double r15583 = r15578 + r15582;
        double r15584 = 0.125;
        double r15585 = v;
        double r15586 = r15579 * r15585;
        double r15587 = r15578 - r15586;
        double r15588 = r15584 * r15587;
        double r15589 = w;
        double r15590 = r15589 * r15589;
        double r15591 = r15590 * r15580;
        double r15592 = r15591 * r15580;
        double r15593 = r15588 * r15592;
        double r15594 = 1.0;
        double r15595 = r15594 - r15585;
        double r15596 = r15593 / r15595;
        double r15597 = r15583 - r15596;
        double r15598 = 4.5;
        double r15599 = r15597 - r15598;
        return r15599;
}
↓
double f(double v, double w, double r) {
        double r15600 = 3.0;
        double r15601 = 2.0;
        double r15602 = r;
        double r15603 = r15602 * r15602;
        double r15604 = r15601 / r15603;
        double r15605 = r15600 + r15604;
        double r15606 = 0.125;
        double r15607 = v;
        double r15608 = r15601 * r15607;
        double r15609 = r15600 - r15608;
        double r15610 = r15606 * r15609;
        double r15611 = w;
        double r15612 = r15611 * r15602;
        double r15613 = fabs(r15612);
        double r15614 = 1.0;
        double r15615 = r15614 - r15607;
        double r15616 = r15615 / r15613;
        double r15617 = r15613 / r15616;
        double r15618 = r15610 * r15617;
        double r15619 = r15605 - r15618;
        double r15620 = 4.5;
        double r15621 = r15619 - r15620;
        return r15621;
}

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. Simplified6.8

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

  7. Applied *-un-lft-identity6.8

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied unpow20.4

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

  13. Applied associate-/l*0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2020039 
(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))