Error

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. 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 *-un-lft-identity0.4

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

5. Applied add-sqr-sqrt0.9

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

6. Applied prod-diff0.9

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

7. Simplified0.3

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

8. Simplified0.3

   \[\leadsto (\left(\frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right))_* + \color{blue}{0}\]
9. Using strategy rm

10. Applied fma-udef0.3

    \[\leadsto \color{blue}{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right)\right)} + 0\]
11. Using strategy rm

12. Applied add-cbrt-cube0.4

    \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right)\right) + 0\]
13. Using strategy rm

14. Applied add-sqr-sqrt0.5

    \[\leadsto \left(\color{blue}{\left(\sqrt{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}} \cdot \sqrt{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}}\right)} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right)\right) + 0\]

15. Applied associate-*l*0.5

    \[\leadsto \left(\color{blue}{\sqrt{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}} \cdot \left(\sqrt{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right)\right)} + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right)\right) + 0\]

16. Simplified0.4

    \[\leadsto \left(\color{blue}{\sqrt{\frac{(-2 \cdot v + 3)_*}{1 - v}}} \cdot \left(\sqrt{\sqrt[3]{\left(\frac{(v \cdot -2 + 3)_*}{1 - v} \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}\right) \cdot \frac{(v \cdot -2 + 3)_*}{1 - v}}} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(-0.125\right)\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{\frac{2}{r}}{r}\right)\right) + 0\]

17. Final simplification0.4

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

Runtime

Time bar (total: 55.8s)Debug logProfile

herbie shell --seed 2018354 +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))