Average Error: 12.8 → 1.0
Time: 33.1s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{\left(0.375 - 0.25 \cdot v\right) \cdot \frac{r \cdot w}{\sqrt[3]{1 - v}}}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w}}\]
\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
↓
\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{\left(0.375 - 0.25 \cdot v\right) \cdot \frac{r \cdot w}{\sqrt[3]{1 - v}}}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w}}
(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
 (-
  (+ (/ 2.0 (* r r)) -1.5)
  (/
   (* (- 0.375 (* 0.25 v)) (/ (* r w) (cbrt (- 1.0 v))))
   (/ (* (cbrt (- 1.0 v)) (cbrt (- 1.0 v))) (* r 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) {
	return ((2.0 / (r * r)) + -1.5) - (((0.375 - (0.25 * v)) * ((r * w) / cbrt(1.0 - v))) / ((cbrt(1.0 - v) * cbrt(1.0 - v)) / (r * w)));
}

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. Initial program 12.8

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

  2. Simplified8.8

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

  4. Applied associate-*r*_binary643.6

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

  5. Simplified3.6

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

  7. Applied add-cube-cbrt_binary643.7

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

  8. Applied times-frac_binary642.7

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

  9. Applied add-cube-cbrt_binary642.8

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

  10. Applied times-frac_binary641.2

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

  12. Applied add-cube-cbrt_binary641.3

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

  13. Applied *-un-lft-identity_binary641.3

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

  14. Applied times-frac_binary641.3

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

  15. Applied associate-/r*_binary641.1

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

  16. Simplified1.1

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

  18. Applied associate-*l/_binary640.7

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

  19. Applied associate-*r/_binary641.2

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

  20. Simplified1.0

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

  21. Final simplification1.0

    \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \frac{\left(0.375 - 0.25 \cdot v\right) \cdot \frac{r \cdot w}{\sqrt[3]{1 - v}}}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w}}\]

Reproduce

herbie shell --seed 2021027 
(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))