Average Error: 12.6 → 4.8
Time: 8.3s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \le -4.61043928310668405 \cdot 10^{-68} \lor \neg \left(r \le 1.0599308933428764 \cdot 10^{-60}\right):\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(\sqrt[3]{r} \cdot \left(r \cdot \left(0.125 \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right)\right)\right)\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + r \cdot \log \left({\left(e^{r}\right)}^{\left(0.125 \cdot \left(\frac{3 - 2 \cdot v}{1 - v} \cdot \left(w \cdot w\right)\right)\right)}\right)\right)\right)\\ \end{array}\]
\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 -4.61043928310668405 \cdot 10^{-68} \lor \neg \left(r \le 1.0599308933428764 \cdot 10^{-60}\right):\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(\sqrt[3]{r} \cdot \left(r \cdot \left(0.125 \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right)\right)\right)\right)\right) + 4.5\right)\right)\\

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

\end{array}
double code(double v, double w, double r) {
	return ((double) (((double) (((double) (3.0 + ((double) (2.0 / ((double) (r * r)))))) - ((double) (((double) (((double) (0.125 * ((double) (3.0 - ((double) (2.0 * v)))))) * ((double) (((double) (((double) (w * w)) * r)) * r)))) / ((double) (1.0 - v)))))) - 4.5));
}
↓
double code(double v, double w, double r) {
	double VAR;
	if (((r <= -4.610439283106684e-68) || !(r <= 1.0599308933428764e-60))) {
		VAR = ((double) (3.0 + ((double) (((double) (2.0 / ((double) (r * r)))) - ((double) (((double) (((double) cbrt(r)) * ((double) (r * ((double) (0.125 * ((double) (((double) cbrt(r)) * ((double) (w * ((double) (w * ((double) (((double) cbrt(r)) * ((double) (((double) (3.0 - ((double) (2.0 * v)))) / ((double) (1.0 - v)))))))))))))))))) + 4.5))))));
	} else {
		VAR = ((double) (3.0 + ((double) (((double) (2.0 / ((double) (r * r)))) - ((double) (4.5 + ((double) (r * ((double) log(((double) pow(((double) exp(r)), ((double) (0.125 * ((double) (((double) (((double) (3.0 - ((double) (2.0 * v)))) / ((double) (1.0 - v)))) * ((double) (w * w))))))))))))))))));
	}
	return VAR;
}

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 < -4.61043928310668405e-68 or 1.0599308933428764e-60 < r

    1. Initial program 12.1

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

    2. Simplified6.5

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

    4. Applied add-cube-cbrt6.8

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

    5. Applied associate-*l*6.8

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

    6. Simplified6.8

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

    8. Applied associate-*l*6.8

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

    9. Simplified4.1

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

    if -4.61043928310668405e-68 < r < 1.0599308933428764e-60

    1. Initial program 13.8

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

    2. Simplified13.4

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

    4. Applied add-cube-cbrt13.4

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

    5. Applied associate-*l*13.4

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

    6. Simplified13.4

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

    8. Applied add-log-exp24.3

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

    9. Simplified6.3

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

  4. Final simplification4.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \le -4.61043928310668405 \cdot 10^{-68} \lor \neg \left(r \le 1.0599308933428764 \cdot 10^{-60}\right):\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(\sqrt[3]{r} \cdot \left(r \cdot \left(0.125 \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right)\right)\right)\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + r \cdot \log \left({\left(e^{r}\right)}^{\left(0.125 \cdot \left(\frac{3 - 2 \cdot v}{1 - v} \cdot \left(w \cdot w\right)\right)\right)}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))