Average Error: 12.6 → 0.6
Time: 6.3s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \leq -1.962133336738353 \cdot 10^{+134}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r}{1 - v} \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\ \mathbf{elif}\;r \leq 8.120287775346159 \cdot 10^{+82}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(r \cdot w\right) \cdot \frac{r}{\frac{1 - v}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(w \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{r}{1 - v} \cdot \left(0.375 + v \cdot -0.25\right)\right)\\ \end{array}\]
\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}\;r \leq -1.962133336738353 \cdot 10^{+134}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r}{1 - v} \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\

\mathbf{elif}\;r \leq 8.120287775346159 \cdot 10^{+82}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(r \cdot w\right) \cdot \frac{r}{\frac{1 - v}{w}}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(w \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{r}{1 - v} \cdot \left(0.375 + v \cdot -0.25\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 (<= r -1.962133336738353e+134)
   (-
    (+ (/ 2.0 (* r r)) -1.5)
    (* (/ r (- 1.0 v)) (* (+ 0.375 (* v -0.25)) (* w (* r w)))))
   (if (<= r 8.120287775346159e+82)
     (-
      (+ (/ 2.0 (* r r)) -1.5)
      (* (+ 0.375 (* v -0.25)) (* (* r w) (/ r (/ (- 1.0 v) w)))))
     (-
      (+ (/ 2.0 (* r r)) -1.5)
      (* (* w (* r w)) (* (/ r (- 1.0 v)) (+ 0.375 (* v -0.25))))))))
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 (r <= -1.962133336738353e+134) {
		tmp = ((2.0 / (r * r)) + -1.5) - ((r / (1.0 - v)) * ((0.375 + (v * -0.25)) * (w * (r * w))));
	} else if (r <= 8.120287775346159e+82) {
		tmp = ((2.0 / (r * r)) + -1.5) - ((0.375 + (v * -0.25)) * ((r * w) * (r / ((1.0 - v) / w))));
	} else {
		tmp = ((2.0 / (r * r)) + -1.5) - ((w * (r * w)) * ((r / (1.0 - v)) * (0.375 + (v * -0.25))));
	}
	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 3 regimes

  2. if r < -1.96213333673835307e134

    1. Initial program 24.5

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

    2. Simplified18.7

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

    4. Applied associate-*r*_binary646.5

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

    6. Applied associate-/r/_binary640.4

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

    7. Applied associate-*r*_binary640.3

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

    8. Simplified0.3

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

    10. Applied associate-*l*_binary641.7

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

    11. Simplified1.7

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

    if -1.96213333673835307e134 < r < 8.1202877753461588e82

    1. Initial program 9.2

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

    2. Simplified6.1

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

    4. Applied associate-*r*_binary643.2

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

    6. Applied *-un-lft-identity_binary643.2

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

    7. Applied times-frac_binary641.9

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

    8. Applied *-un-lft-identity_binary641.9

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

    9. Applied times-frac_binary640.5

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

    10. Simplified0.5

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

    if 8.1202877753461588e82 < r

    1. Initial program 18.5

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

    2. Simplified12.5

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

    4. Applied associate-*r*_binary643.8

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

    6. Applied associate-/r/_binary640.4

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

    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

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \leq -1.962133336738353 \cdot 10^{+134}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r}{1 - v} \cdot \left(\left(0.375 + v \cdot -0.25\right) \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\ \mathbf{elif}\;r \leq 8.120287775346159 \cdot 10^{+82}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(r \cdot w\right) \cdot \frac{r}{\frac{1 - v}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(w \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{r}{1 - v} \cdot \left(0.375 + v \cdot -0.25\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020280 
(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))