Error

Derivation

1. Initial program 12.6

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

3. Applied *-un-lft-identity12.6

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

4. Applied associate-/r*12.6

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

5. Applied simplify6.3

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

7. Applied add-cube-cbrt6.4

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

8. Applied times-frac6.4

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

10. Applied *-un-lft-identity6.4

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

11. Applied times-frac4.3

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

12. Applied associate-*r*0.5

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

13. Applied simplify0.5

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

15. Applied *-un-lft-identity0.5

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

16. Applied cbrt-prod0.5

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

17. Applied add-cube-cbrt0.5

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

18. Applied times-frac0.5

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

19. Applied associate-*r*0.5

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

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))