Average Error: 13.5 → 0.4
Time: 11.1s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \le -4.3369554949408822 \cdot 10^{63} \lor \neg \left(r \le 9.091653763374461 \cdot 10^{186}\right):\\ \;\;\;\;\left(\left(3 + \sqrt{\frac{2}{r \cdot r}} \cdot \frac{\sqrt{2}}{\left|r\right|}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\\ \end{array}\]
\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 -4.3369554949408822 \cdot 10^{63} \lor \neg \left(r \le 9.091653763374461 \cdot 10^{186}\right):\\
\;\;\;\;\left(\left(3 + \sqrt{\frac{2}{r \cdot r}} \cdot \frac{\sqrt{2}}{\left|r\right|}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\\

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

\end{array}
double code(double v, double w, double r) {
	return ((double) (((double) (((double) (3.0 + (2.0 / ((double) (r * r))))) - (((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 <= -4.336955494940882e+63) || !(r <= 9.091653763374461e+186))) {
		VAR = ((double) (((double) (((double) (3.0 + ((double) (((double) sqrt((2.0 / ((double) (r * r))))) * (((double) sqrt(2.0)) / ((double) fabs(r))))))) - ((double) (((double) (0.125 * ((double) (3.0 - ((double) (2.0 * v)))))) * (((double) (((double) (w * ((double) (w * r)))) * r)) / ((double) (1.0 - v))))))) - 4.5));
	} else {
		VAR = ((double) (((double) (((double) (3.0 + (2.0 / ((double) (r * r))))) - ((double) (((double) (0.125 * ((double) (3.0 - ((double) (2.0 * v)))))) * (((double) (w * ((double) (((double) (w * r)) * r)))) / ((double) (1.0 - v))))))) - 4.5));
	}
	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 < -4.3369554949408822e63 or 9.091653763374461e186 < r

    1. Initial program 22.6

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

    3. Applied associate-*l*10.4

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

    5. Applied *-un-lft-identity10.4

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

    6. Applied times-frac0.4

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

    7. Simplified0.4

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

    9. Applied add-sqr-sqrt0.4

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

    11. Applied sqrt-div0.4

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

    12. Simplified0.4

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

    if -4.3369554949408822e63 < r < 9.091653763374461e186

    1. Initial program 10.3

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

    3. Applied associate-*l*8.0

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

    5. Applied *-un-lft-identity8.0

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

    6. Applied times-frac3.5

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

    7. Simplified3.5

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

    9. Applied associate-*l*0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \le -4.3369554949408822 \cdot 10^{63} \lor \neg \left(r \le 9.091653763374461 \cdot 10^{186}\right):\\ \;\;\;\;\left(\left(3 + \sqrt{\frac{2}{r \cdot r}} \cdot \frac{\sqrt{2}}{\left|r\right|}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{w \cdot \left(\left(w \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))