Average Error: 11.8 → 1.2
Time: 2.7m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(\left(0.125 \cdot \left(\sqrt[3]{3 - 2 \cdot v} \cdot \sqrt[3]{3 - 2 \cdot v}\right)\right) \cdot 1\right) \cdot \left(\left(w \cdot r\right) \cdot 1\right)}{\left(\frac{\sqrt[3]{1 - v}}{\sqrt[3]{3 - 2 \cdot v}} \cdot \frac{\sqrt[3]{1 - v}}{w}\right) \cdot \frac{\sqrt[3]{1 - v}}{r}}\right) - 4.5\]
\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{2}{r \cdot r}\right) - \frac{\left(\left(0.125 \cdot \left(\sqrt[3]{3 - 2 \cdot v} \cdot \sqrt[3]{3 - 2 \cdot v}\right)\right) \cdot 1\right) \cdot \left(\left(w \cdot r\right) \cdot 1\right)}{\left(\frac{\sqrt[3]{1 - v}}{\sqrt[3]{3 - 2 \cdot v}} \cdot \frac{\sqrt[3]{1 - v}}{w}\right) \cdot \frac{\sqrt[3]{1 - v}}{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) (2.0 / ((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)))))))))) * 1.0)) * ((double) (((double) (w * r)) * 1.0)))) / ((double) (((double) (((double) (((double) cbrt(((double) (1.0 - v)))) / ((double) cbrt(((double) (3.0 - ((double) (2.0 * v)))))))) * ((double) (((double) cbrt(((double) (1.0 - v)))) / w)))) * ((double) (((double) cbrt(((double) (1.0 - v)))) / 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 11.8

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

  3. Applied add-cube-cbrt11.9

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

  4. Applied associate-*l*7.6

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

  5. Applied associate-*l*9.0

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

  6. Applied associate-*r*9.6

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

  7. Applied times-frac6.9

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

  8. Simplified4.7

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

  10. Applied *-un-lft-identity4.7

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

  11. Applied associate-*r*4.7

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

  12. Applied associate-/l*3.8

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

  13. Applied clear-num3.8

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

  14. Applied add-cube-cbrt3.8

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

  15. Applied associate-*r*3.8

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

  16. Applied associate-/l*3.8

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

  17. Applied frac-times3.8

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

  18. Applied frac-times1.2

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

  19. Final simplification1.2

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

Reproduce

herbie shell --seed 2020113 
(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))