Average Error: 12.3 → 0.4
Time: 6.1s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 7.566514815671635 \cdot 10^{+241}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \left(\sqrt[3]{\sqrt[3]{r} \cdot \sqrt[3]{r}} \cdot \sqrt[3]{\sqrt[3]{r}}\right)\right)\right)\right) \cdot \left(\left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right) \cdot \sqrt[3]{r}\right) - 4.5\right)\right)\\ \end{array}\]
\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 \cdot w \leq 7.566514815671635 \cdot 10^{+241}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(\left(w \cdot r\right) \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{else}:\\
\;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \left(\sqrt[3]{\sqrt[3]{r} \cdot \sqrt[3]{r}} \cdot \sqrt[3]{\sqrt[3]{r}}\right)\right)\right)\right) \cdot \left(\left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right) \cdot \sqrt[3]{r}\right) - 4.5\right)\right)\\

\end{array}
(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))
↓
(FPCore (v w r)
 :precision binary64
 (if (<= (* w w) 7.566514815671635e+241)
   (+
    3.0
    (+
     (/ 2.0 (* r r))
     (-
      (* r (* (* w r) (* w (* (/ 0.125 (- 1.0 v)) (- (* 2.0 v) 3.0)))))
      4.5)))
   (+
    3.0
    (+
     (/ 2.0 (* r r))
     (-
      (*
       (*
        r
        (* w (* (cbrt r) (* (cbrt (* (cbrt r) (cbrt r))) (cbrt (cbrt r))))))
       (* (* w (* (/ 0.125 (- 1.0 v)) (- (* 2.0 v) 3.0))) (cbrt r)))
      4.5)))))
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 tmp;
	if ((((double) (w * w)) <= 7.566514815671635e+241)) {
		tmp = ((double) (3.0 + ((double) ((2.0 / ((double) (r * r))) + ((double) (((double) (r * ((double) (((double) (w * r)) * ((double) (w * ((double) ((0.125 / ((double) (1.0 - v))) * ((double) (((double) (2.0 * v)) - 3.0)))))))))) - 4.5))))));
	} else {
		tmp = ((double) (3.0 + ((double) ((2.0 / ((double) (r * r))) + ((double) (((double) (((double) (r * ((double) (w * ((double) (((double) cbrt(r)) * ((double) (((double) cbrt(((double) (((double) cbrt(r)) * ((double) cbrt(r)))))) * ((double) cbrt(((double) cbrt(r)))))))))))) * ((double) (((double) (w * ((double) ((0.125 / ((double) (1.0 - v))) * ((double) (((double) (2.0 * v)) - 3.0)))))) * ((double) cbrt(r)))))) - 4.5))))));
	}
	return tmp;
}

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) < 7.56651481567163466e241

    1. Initial program Error: 8.2 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: 4.3 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 associate-*l*Error: 0.3 bits

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

    7. SimplifiedError: 0.3 bits

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

    if 7.56651481567163466e241 < (* w w)

    1. Initial program Error: 49.0 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: 44.4 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: 22.1 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: 22.4 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: 22.4 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: 14.9 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: 1.0 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: 1.0 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 add-cube-cbrtError: 1.1 bits

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

    14. Applied cbrt-prodError: 1.1 bits

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

  4. Final simplificationError: 0.4 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \leq 7.566514815671635 \cdot 10^{+241}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(r \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right)\right) - 4.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 + \left(\frac{2}{r \cdot r} + \left(\left(r \cdot \left(w \cdot \left(\sqrt[3]{r} \cdot \left(\sqrt[3]{\sqrt[3]{r} \cdot \sqrt[3]{r}} \cdot \sqrt[3]{\sqrt[3]{r}}\right)\right)\right)\right) \cdot \left(\left(w \cdot \left(\frac{0.125}{1 - v} \cdot \left(2 \cdot v - 3\right)\right)\right) \cdot \sqrt[3]{r}\right) - 4.5\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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))