Average Error: 12.8 → 0.3
Time: 11.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\ \end{array}\]
\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
↓
\begin{array}{l}
\mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\
\;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\

\mathbf{else}:\\
\;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\

\end{array}
double f(double v, double w, double r) {
        double r17386 = 3.0;
        double r17387 = 2.0;
        double r17388 = r;
        double r17389 = r17388 * r17388;
        double r17390 = r17387 / r17389;
        double r17391 = r17386 + r17390;
        double r17392 = 0.125;
        double r17393 = v;
        double r17394 = r17387 * r17393;
        double r17395 = r17386 - r17394;
        double r17396 = r17392 * r17395;
        double r17397 = w;
        double r17398 = r17397 * r17397;
        double r17399 = r17398 * r17388;
        double r17400 = r17399 * r17388;
        double r17401 = r17396 * r17400;
        double r17402 = 1.0;
        double r17403 = r17402 - r17393;
        double r17404 = r17401 / r17403;
        double r17405 = r17391 - r17404;
        double r17406 = 4.5;
        double r17407 = r17405 - r17406;
        return r17407;
}
↓
double f(double v, double w, double r) {
        double r17408 = r;
        double r17409 = -6.832602897595849e-09;
        bool r17410 = r17408 <= r17409;
        double r17411 = 3.482628925649384e+139;
        bool r17412 = r17408 <= r17411;
        double r17413 = !r17412;
        bool r17414 = r17410 || r17413;
        double r17415 = 3.0;
        double r17416 = 2.0;
        double r17417 = r17416 / r17408;
        double r17418 = r17417 / r17408;
        double r17419 = r17415 + r17418;
        double r17420 = 0.125;
        double r17421 = v;
        double r17422 = r17416 * r17421;
        double r17423 = r17415 - r17422;
        double r17424 = r17420 * r17423;
        double r17425 = 1.0;
        double r17426 = r17425 - r17421;
        double r17427 = r17424 / r17426;
        double r17428 = w;
        double r17429 = r17428 * r17408;
        double r17430 = r17428 * r17429;
        double r17431 = r17430 * r17408;
        double r17432 = r17427 * r17431;
        double r17433 = r17419 - r17432;
        double r17434 = 4.5;
        double r17435 = r17433 - r17434;
        double r17436 = r17429 * r17408;
        double r17437 = r17428 * r17436;
        double r17438 = r17426 / r17437;
        double r17439 = r17424 / r17438;
        double r17440 = r17419 - r17439;
        double r17441 = r17440 - r17434;
        double r17442 = r17414 ? r17435 : r17441;
        return r17442;
}

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. Split input into 2 regimes

  2. if r < -6.832602897595849e-09 or 3.482628925649384e+139 < r

    1. Initial program 17.3

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

    3. Applied associate-*l*9.0

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

    5. Applied associate-/l*0.3

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

    7. Applied associate-/r*0.3

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

    9. Applied associate-/r/0.2

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

    if -6.832602897595849e-09 < r < 3.482628925649384e+139

    1. Initial program 10.1

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

    3. Applied associate-*l*7.7

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

    5. Applied associate-/l*4.0

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

    7. Applied associate-/r*4.0

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

    9. Applied associate-*l*0.3

      \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\color{blue}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}}\right) - 4.5\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \le -6.832602897595849 \cdot 10^{-9} \lor \neg \left(r \le 3.482628925649384 \cdot 10^{139}\right):\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}}\right) - 4.5\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))