Average Error: 12.4 → 0.3
Time: 6.5s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;r \leq -9.302112022616566 \cdot 10^{+59}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{0.375 + v \cdot -0.25}{1 - v} \cdot \frac{r}{\frac{1}{w \cdot \left(r \cdot w\right)}}\\ \mathbf{elif}\;r \leq 8.580410111110405 \cdot 10^{-05}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(r \cdot w\right)}{\frac{1 - v}{w}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(w \cdot \left(r \cdot w\right)\right) \cdot \frac{r}{1 - v}\right)\\ \end{array}\]
\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 -9.302112022616566 \cdot 10^{+59}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{0.375 + v \cdot -0.25}{1 - v} \cdot \frac{r}{\frac{1}{w \cdot \left(r \cdot w\right)}}\\

\mathbf{elif}\;r \leq 8.580410111110405 \cdot 10^{-05}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(r \cdot w\right)}{\frac{1 - v}{w}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(w \cdot \left(r \cdot w\right)\right) \cdot \frac{r}{1 - v}\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 -9.302112022616566e+59)
   (-
    (+ (/ 2.0 (* r r)) -1.5)
    (* (/ (+ 0.375 (* v -0.25)) (- 1.0 v)) (/ r (/ 1.0 (* w (* r w))))))
   (if (<= r 8.580410111110405e-05)
     (-
      (+ (/ 2.0 (* r r)) -1.5)
      (* (+ 0.375 (* v -0.25)) (/ (* r (* r w)) (/ (- 1.0 v) w))))
     (-
      (+ (/ 2.0 (* r r)) -1.5)
      (* (+ 0.375 (* v -0.25)) (* (* w (* r w)) (/ r (- 1.0 v))))))))
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 <= -9.302112022616566e+59) {
		tmp = ((2.0 / (r * r)) + -1.5) - (((0.375 + (v * -0.25)) / (1.0 - v)) * (r / (1.0 / (w * (r * w)))));
	} else if (r <= 8.580410111110405e-05) {
		tmp = ((2.0 / (r * r)) + -1.5) - ((0.375 + (v * -0.25)) * ((r * (r * w)) / ((1.0 - v) / w)));
	} else {
		tmp = ((2.0 / (r * r)) + -1.5) - ((0.375 + (v * -0.25)) * ((w * (r * w)) * (r / (1.0 - v))));
	}
	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 < -9.30211202261656637e59

    1. Initial program 17.7

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

    2. Simplified11.5

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

    4. Applied associate-*r*_binary644.4

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

    6. Applied div-inv_binary644.4

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

    7. Applied *-un-lft-identity_binary644.4

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

    8. Applied times-frac_binary640.3

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

    9. Applied associate-*r*_binary640.3

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

    10. Simplified0.3

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

    if -9.30211202261656637e59 < r < 8.5804101111104048e-5

    1. Initial program 10.0

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

    2. Simplified7.9

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

    4. Applied associate-*r*_binary644.2

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

    6. Applied *-un-lft-identity_binary644.2

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

    7. Applied times-frac_binary642.3

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

    8. Applied associate-/r*_binary640.3

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

    9. Simplified0.3

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

    if 8.5804101111104048e-5 < r

    1. Initial program 13.6

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

    2. Simplified7.1

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

    4. Applied associate-*r*_binary642.4

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

    6. Applied associate-/r/_binary640.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \leq -9.302112022616566 \cdot 10^{+59}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{0.375 + v \cdot -0.25}{1 - v} \cdot \frac{r}{\frac{1}{w \cdot \left(r \cdot w\right)}}\\ \mathbf{elif}\;r \leq 8.580410111110405 \cdot 10^{-05}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r \cdot \left(r \cdot w\right)}{\frac{1 - v}{w}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\left(w \cdot \left(r \cdot w\right)\right) \cdot \frac{r}{1 - v}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020281 
(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))