Average Error: 12.8 → 0.3
Time: 7.0s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;w \cdot w \le 2.0062619874181415 \cdot 10^{217}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(r \cdot \left(\left(r \cdot \left(w \cdot 0.125\right)\right) \cdot \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right) \cdot \left(r \cdot \left(r \cdot \left(w \cdot 0.125\right)\right)\right)\right)\right)\\ \end{array}\]
\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 2.0062619874181415 \cdot 10^{217}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(r \cdot \left(\left(r \cdot \left(w \cdot 0.125\right)\right) \cdot \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right) + 4.5\right)\right)\\

\mathbf{else}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right) \cdot \left(r \cdot \left(r \cdot \left(w \cdot 0.125\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)) <= 2.0062619874181415e+217)) {
		VAR = ((double) (3.0 + ((double) (((double) (2.0 / ((double) (r * r)))) - ((double) (((double) (r * ((double) (((double) (r * ((double) (w * 0.125)))) * ((double) (w * ((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) (((double) (w * ((double) (((double) (3.0 - ((double) (2.0 * v)))) / ((double) (1.0 - v)))))) * ((double) (r * ((double) (r * ((double) (w * 0.125))))))))))))));
	}
	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) < 2.0062619874181415e217

    1. Initial program 8.8

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

    2. Simplified4.6

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

    4. Applied associate-*r*4.6

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

    6. Applied associate-*r*0.3

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

    7. Simplified0.3

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

    if 2.0062619874181415e217 < (* w w)

    1. Initial program 43.2

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

    2. Simplified37.3

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

    4. Applied associate-*r*37.3

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

    6. Applied associate-*r*19.2

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

    7. Simplified19.2

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

    9. Applied associate-*r*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \le 2.0062619874181415 \cdot 10^{217}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(r \cdot \left(\left(r \cdot \left(w \cdot 0.125\right)\right) \cdot \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right) + 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} - \left(4.5 + \left(w \cdot \frac{3 - 2 \cdot v}{1 - v}\right) \cdot \left(r \cdot \left(r \cdot \left(w \cdot 0.125\right)\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))