Average Error: 13.0 → 0.4
Time: 6.0s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;w \cdot w \le 4.7325497700359403 \cdot 10^{295}:\\ \;\;\;\;3 + \left(\frac{\frac{2}{r}}{r} - \left(r \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)\right)\right)\right)\right)\\ \end{array}\]
\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}\;w \cdot w \le 4.7325497700359403 \cdot 10^{295}:\\
\;\;\;\;3 + \left(\frac{\frac{2}{r}}{r} - \left(r \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)\right) + 4.5\right)\right)\\

\mathbf{else}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\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 ((((double) (w * w)) <= 4.73254977003594e+295)) {
		VAR = ((double) (3.0 + ((double) (((double) (((double) (2.0 / r)) / r)) - ((double) (((double) (r * ((double) (((double) (w * ((double) (w * r)))) * ((double) (((double) (0.125 / ((double) (1.0 - v)))) * ((double) (3.0 - ((double) (2.0 * v)))))))))) + 4.5))))));
	} else {
		VAR = ((double) (3.0 + ((double) (((double) (2.0 / ((double) (r * r)))) - ((double) (4.5 + ((double) (((double) (r * ((double) (w * ((double) (((double) cbrt(r)) * ((double) cbrt(r)))))))) * ((double) (((double) cbrt(r)) * ((double) (w * ((double) (((double) (0.125 / ((double) (1.0 - v)))) * ((double) (3.0 - ((double) (2.0 * v))))))))))))))))));
	}
	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 (* w w) < 4.7325497700359403e295

    1. Initial program 9.4

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

    2. Simplified4.7

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

    4. Applied associate-*r*0.3

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

    6. Applied associate-/r*0.3

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

    if 4.7325497700359403e295 < (* w w)

    1. Initial program 60.4

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

    2. Simplified59.4

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

    4. Applied associate-*r*28.8

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

    6. Applied add-cube-cbrt29.0

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

    7. Applied associate-*l*29.0

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

    8. Simplified20.2

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

    10. Applied associate-*r*0.9

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

    11. Simplified0.9

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \le 4.7325497700359403 \cdot 10^{295}:\\ \;\;\;\;3 + \left(\frac{\frac{2}{r}}{r} - \left(r \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))