Average Error: 12.6 → 0.4
Time: 10.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left|w \cdot r\right| \cdot \left|w \cdot r\right|\right)\right) - 4.5\]
\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)}{1 - v} \cdot \left(\left|w \cdot r\right| \cdot \left|w \cdot r\right|\right)\right) - 4.5
double f(double v, double w, double r) {
        double r15558 = 3.0;
        double r15559 = 2.0;
        double r15560 = r;
        double r15561 = r15560 * r15560;
        double r15562 = r15559 / r15561;
        double r15563 = r15558 + r15562;
        double r15564 = 0.125;
        double r15565 = v;
        double r15566 = r15559 * r15565;
        double r15567 = r15558 - r15566;
        double r15568 = r15564 * r15567;
        double r15569 = w;
        double r15570 = r15569 * r15569;
        double r15571 = r15570 * r15560;
        double r15572 = r15571 * r15560;
        double r15573 = r15568 * r15572;
        double r15574 = 1.0;
        double r15575 = r15574 - r15565;
        double r15576 = r15573 / r15575;
        double r15577 = r15563 - r15576;
        double r15578 = 4.5;
        double r15579 = r15577 - r15578;
        return r15579;
}
↓
double f(double v, double w, double r) {
        double r15580 = 3.0;
        double r15581 = 2.0;
        double r15582 = r;
        double r15583 = r15582 * r15582;
        double r15584 = r15581 / r15583;
        double r15585 = r15580 + r15584;
        double r15586 = 0.125;
        double r15587 = v;
        double r15588 = r15581 * r15587;
        double r15589 = r15580 - r15588;
        double r15590 = r15586 * r15589;
        double r15591 = 1.0;
        double r15592 = r15591 - r15587;
        double r15593 = r15590 / r15592;
        double r15594 = w;
        double r15595 = r15594 * r15582;
        double r15596 = fabs(r15595);
        double r15597 = r15596 * r15596;
        double r15598 = r15593 * r15597;
        double r15599 = r15585 - r15598;
        double r15600 = 4.5;
        double r15601 = r15599 - r15600;
        return r15601;
}

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 12.6

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

  3. Applied associate-/l*8.4

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

  5. Applied associate-*l*2.4

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

  7. Applied add-sqr-sqrt2.5

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

  8. Simplified2.5

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

  9. Simplified0.4

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

  11. Applied associate-/r/0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 
(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))