Average Error: 12.5 → 0.3
Time: 16.5s
Precision: binary64
Cost: 2049
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 2.4955352936326524 \cdot 10^{+38}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(w \cdot r\right)}{\frac{1 - v}{w}}\\ \end{array}\]
\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 2.4955352936326524 \cdot 10^{+38}:\\
\;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{1 - v}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(w \cdot r\right)}{\frac{1 - v}{w}}\\

\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) 2.4955352936326524e+38)
   (-
    (+ -1.5 (/ 2.0 (* r r)))
    (* (* w (* w r)) (* (+ 0.375 (* v -0.25)) (/ r (- 1.0 v)))))
   (-
    (+ -1.5 (/ 2.0 (* r r)))
    (* (+ 0.375 (* v -0.25)) (/ (* r (* w r)) (/ (- 1.0 v) w))))))
double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}
↓
double code(double v, double w, double r) {
	double tmp;
	if ((w * w) <= 2.4955352936326524e+38) {
		tmp = (-1.5 + (2.0 / (r * r))) - ((w * (w * r)) * ((0.375 + (v * -0.25)) * (r / (1.0 - v))));
	} else {
		tmp = (-1.5 + (2.0 / (r * r))) - ((0.375 + (v * -0.25)) * ((r * (w * r)) / ((1.0 - v) / w)));
	}
	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

Alternatives

Alternative 1
Error0.8
Cost21312
\[\left(-1.5 + \frac{2}{r \cdot r}\right) - \frac{r}{\frac{\sqrt[3]{1 - v}}{w}} \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{w \cdot r}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}\right)\]
Alternative 2
Error0.8
Cost21312
\[\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\frac{r}{\frac{\sqrt[3]{1 - v}}{w}} \cdot \frac{w \cdot r}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}\right)\]
Alternative 3
Error0.3
Cost1928
\[\begin{array}{l} \mathbf{if}\;v \leq -3.806672820169377 \cdot 10^{+23} \lor \neg \left(v \leq 3.2366970952931783 \cdot 10^{+41}\right):\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot r\right) \cdot \left(0.375 + v \cdot -0.25\right)\right) \cdot \frac{r}{\frac{1 - v}{w}}\\ \end{array}\]
Alternative 4
Error0.8
Cost1416
\[\begin{array}{l} \mathbf{if}\;v \leq -12391569.29492999 \lor \neg \left(v \leq 0.9608221583659738\right):\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\\ \end{array}\]
Alternative 5
Error1.7
Cost1416
\[\begin{array}{l} \mathbf{if}\;v \leq -12391569.29492999 \lor \neg \left(v \leq 0.7324601245828686\right):\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left(r \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)\\ \end{array}\]
Alternative 6
Error2.8
Cost1416
\[\begin{array}{l} \mathbf{if}\;v \leq -12391569.29492999 \lor \neg \left(v \leq 1.0129891302451897\right):\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.25 \cdot \left(r \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left(r \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)\\ \end{array}\]
Alternative 7
Error5.7
Cost1416
\[\begin{array}{l} \mathbf{if}\;v \leq -110201753769437.28 \lor \neg \left(v \leq 9.315081571616325\right):\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.25 \cdot \left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left(r \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)\\ \end{array}\]
Alternative 8
Error10.6
Cost1088
\[\left(-1.5 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left(r \cdot \left(w \cdot \left(w \cdot r\right)\right)\right)\]
Alternative 9
Error59.1
Cost64
\[-1\]
Alternative 10
Error62.3
Cost64
\[1\]

Error

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 w w) < 2.49553529363265239e38

    1. Initial program 8.4

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

    2. Simplified5.7

      \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}}}\]
    3. Using strategy rm

    4. Applied associate-*r*_binary642.1

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{\color{blue}{\left(r \cdot w\right) \cdot w}}}\]
    5. Using strategy rm

    6. Applied associate-/r/_binary640.2

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \color{blue}{\left(\frac{r}{1 - v} \cdot \left(\left(r \cdot w\right) \cdot w\right)\right)}\]

    7. Applied associate-*r*_binary640.2

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \color{blue}{\left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{1 - v}\right) \cdot \left(\left(r \cdot w\right) \cdot w\right)}\]

    8. Simplified0.2

      \[\leadsto \color{blue}{\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(w \cdot \left(r \cdot w\right)\right) \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{1 - v}\right)}\]

    if 2.49553529363265239e38 < (*.f64 w w)

    1. Initial program 25.9

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

    2. Simplified18.3

      \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}}}\]
    3. Using strategy rm

    4. Applied associate-*r*_binary649.4

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{\color{blue}{\left(r \cdot w\right) \cdot w}}}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity_binary649.4

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{\color{blue}{1 \cdot \left(1 - v\right)}}{\left(r \cdot w\right) \cdot w}}\]

    7. Applied times-frac_binary644.3

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\color{blue}{\frac{1}{r \cdot w} \cdot \frac{1 - v}{w}}}\]

    8. Applied associate-/r*_binary640.5

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \color{blue}{\frac{\frac{r}{\frac{1}{r \cdot w}}}{\frac{1 - v}{w}}}\]

    9. Simplified0.5

      \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{\color{blue}{r \cdot \left(r \cdot w\right)}}{\frac{1 - v}{w}}\]

    10. Simplified0.5

      \[\leadsto \color{blue}{\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(r \cdot w\right)}{\frac{1 - v}{w}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \leq 2.4955352936326524 \cdot 10^{+38}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(w \cdot \left(w \cdot r\right)\right) \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1.5 + \frac{2}{r \cdot r}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(w \cdot r\right)}{\frac{1 - v}{w}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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))