Average Error: 12.9 → 0.5
Time: 3.1m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{\left|r\right|}}{\sqrt{r \cdot r}}\right) - \frac{\frac{0.125 \cdot \left(\sqrt[3]{3 - 2 \cdot v} \cdot \sqrt[3]{3 - 2 \cdot v}\right)}{\sqrt[3]{1}}}{\left(-\sqrt[3]{1 - v}\right) \cdot \sqrt[3]{1 - v}} \cdot \frac{\left(\frac{\sqrt[3]{3 - 2 \cdot v}}{\sqrt[3]{1 - v}} \cdot \left(-w\right)\right) \cdot r}{\frac{1}{w \cdot r}}\right) - 4.5\]
\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
↓
\left(\left(3 + \frac{\frac{2}{\left|r\right|}}{\sqrt{r \cdot r}}\right) - \frac{\frac{0.125 \cdot \left(\sqrt[3]{3 - 2 \cdot v} \cdot \sqrt[3]{3 - 2 \cdot v}\right)}{\sqrt[3]{1}}}{\left(-\sqrt[3]{1 - v}\right) \cdot \sqrt[3]{1 - v}} \cdot \frac{\left(\frac{\sqrt[3]{3 - 2 \cdot v}}{\sqrt[3]{1 - v}} \cdot \left(-w\right)\right) \cdot r}{\frac{1}{w \cdot r}}\right) - 4.5
double code(double v, double w, double r) {
	return ((double) (((double) (((double) (3.0 + ((double) (2.0 / ((double) (r * r)))))) - ((double) (((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) {
	return ((double) (((double) (((double) (3.0 + ((double) (((double) (2.0 / ((double) fabs(r)))) / ((double) sqrt(((double) (r * r)))))))) - ((double) (((double) (((double) (((double) (0.125 * ((double) (((double) cbrt(((double) (3.0 - ((double) (2.0 * v)))))) * ((double) cbrt(((double) (3.0 - ((double) (2.0 * v)))))))))) / ((double) cbrt(1.0)))) / ((double) (((double) -(((double) cbrt(((double) (1.0 - v)))))) * ((double) cbrt(((double) (1.0 - v)))))))) * ((double) (((double) (((double) (((double) (((double) cbrt(((double) (3.0 - ((double) (2.0 * v)))))) / ((double) cbrt(((double) (1.0 - v)))))) * ((double) -(w)))) * r)) / ((double) (1.0 / ((double) (w * r)))))))))) - 4.5));
}

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 12.9

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

  3. Applied add-cube-cbrt12.9

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

  4. Applied associate-*l*8.1

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

  5. Applied associate-*l*9.5

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

  6. Applied associate-*r*10.3

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

  7. Applied times-frac7.5

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

  8. Simplified5.0

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

  10. Applied *-commutative5.0

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

  11. Applied associate-*l*5.0

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

  12. Applied associate-/l*4.0

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

  13. Applied frac-2neg4.0

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

  14. Applied associate-*r/4.6

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

  15. Applied frac-times1.9

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

  17. Applied div-inv1.9

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

  18. Applied associate-*r*1.9

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

  19. Applied *-un-lft-identity1.9

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

  20. Applied cbrt-prod1.9

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

  21. Applied add-cube-cbrt1.9

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

  22. Applied associate-*r*1.9

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

  23. Applied times-frac1.9

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

  24. Applied associate-*l*1.9

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

  25. Applied associate-*l*0.9

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

  26. Applied times-frac0.5

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

  28. Applied add-sqr-sqrt0.5

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

  29. Applied associate-/r*0.5

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

  30. Simplified0.5

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

  31. Final simplification0.5

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

Reproduce

herbie shell --seed 2020114 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))