Average Error: 13.0 → 1.0
Time: 6.8s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;w \leq -5.2618586165004995 \cdot 10^{+172}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{elif}\;w \leq 6.946392938258538 \cdot 10^{+153}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(w \cdot \left(r \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\frac{\left(w \cdot \left(r \cdot r\right)\right) \cdot \left(w \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)\right)}{1 - v} - 4.5\right)\right)\\ \end{array}\]
\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 \leq -5.2618586165004995 \cdot 10^{+172}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\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(2 \cdot v - 3\right)\right)\right)\right) - 4.5\right)\right)\\

\mathbf{elif}\;w \leq 6.946392938258538 \cdot 10^{+153}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(w \cdot \left(r \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right)\right) - 4.5\right)\right)\\

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

\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 ((w <= -5.2618586165004995e+172)) {
		VAR = ((double) (3.0 + ((double) ((2.0 / ((double) (r * r))) + ((double) (((double) (((double) (r * ((double) (w * ((double) (((double) cbrt(r)) * ((double) cbrt(r)))))))) * ((double) (((double) cbrt(r)) * ((double) (w * ((double) ((0.125 / ((double) (1.0 - v))) * ((double) (((double) (2.0 * v)) - 3.0)))))))))) - 4.5))))));
	} else {
		double VAR_1;
		if ((w <= 6.946392938258538e+153)) {
			VAR_1 = ((double) (3.0 + ((double) ((2.0 / ((double) (r * r))) + ((double) (((double) (r * ((double) (w * ((double) (r * ((double) (w * ((double) ((0.125 / ((double) (1.0 - v))) * ((double) (((double) (2.0 * v)) - 3.0)))))))))))) - 4.5))))));
		} else {
			VAR_1 = ((double) (3.0 + ((double) ((2.0 / ((double) (r * r))) + ((double) ((((double) (((double) (w * ((double) (r * r)))) * ((double) (w * ((double) (0.125 * ((double) (((double) (2.0 * v)) - 3.0)))))))) / ((double) (1.0 - v))) - 4.5))))));
		}
		VAR = VAR_1;
	}
	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 3 regimes

  2. if w < -5.26185861650049948e172

    1. Initial program Error: 64.0 bits

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

    2. SimplifiedError: 64.0 bits

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

    4. Applied associate-*r*Error: 38.8 bits

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

    6. Applied add-cube-cbrtError: 38.9 bits

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

    7. Applied associate-*l*Error: 38.9 bits

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

    8. SimplifiedError: 26.0 bits

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

    10. Applied associate-*r*Error: 0.9 bits

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

    11. SimplifiedError: 0.9 bits

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

    if -5.26185861650049948e172 < w < 6.946392938258538e153

    1. Initial program Error: 9.8 bits

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

    2. SimplifiedError: 5.0 bits

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

    4. Applied associate-*r*Error: 0.3 bits

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

    6. Applied add-cube-cbrtError: 0.6 bits

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

    7. Applied associate-*l*Error: 0.6 bits

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

    8. SimplifiedError: 0.6 bits

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

    10. Applied associate-*r*Error: 1.3 bits

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

    11. SimplifiedError: 1.3 bits

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

    13. Applied associate-*l*Error: 0.6 bits

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

    14. SimplifiedError: 0.3 bits

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

    if 6.946392938258538e153 < w

    1. Initial program Error: 63.7 bits

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

    2. SimplifiedError: 63.7 bits

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

    4. Applied associate-*r*Error: 27.7 bits

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

    6. Applied add-cube-cbrtError: 27.9 bits

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

    7. Applied associate-*l*Error: 27.9 bits

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

    8. SimplifiedError: 21.7 bits

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

    10. Applied associate-*r*Error: 0.8 bits

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

    11. SimplifiedError: 0.8 bits

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

    13. Applied associate-*l/Error: 0.8 bits

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

    14. Applied associate-*r/Error: 19.5 bits

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

    15. Applied associate-*l/Error: 19.5 bits

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

    16. Applied associate-*r/Error: 22.3 bits

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

    17. SimplifiedError: 22.0 bits

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

  4. Final simplificationError: 1.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -5.2618586165004995 \cdot 10^{+172}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \sqrt[3]{r}\right)\right)\right) \cdot \left(\sqrt[3]{r} \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{elif}\;w \leq 6.946392938258538 \cdot 10^{+153}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(w \cdot \left(r \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\frac{\left(w \cdot \left(r \cdot r\right)\right) \cdot \left(w \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)\right)}{1 - v} - 4.5\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))