Error

Derivation

1. Initial program 12.3

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

2. Initial simplification0.4

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

4. Applied associate-/r*0.4

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

6. Applied add-cbrt-cube7.4

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

7. Applied add-cbrt-cube21.0

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

8. Applied cbrt-undiv21.0

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

9. Simplified0.4

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

11. Applied div-inv0.4

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

12. Applied cube-prod0.4

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

13. Applied cbrt-prod0.4

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

14. Simplified0.4

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

15. Final simplification0.4

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

Runtime

Time bar (total: 35.7s)Debug logProfile

herbie shell --seed 2018290 +o rules:numerics
(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))