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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

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

4. Applied div-inv0.4

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

5. Applied times-frac0.4

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

6. Simplified0.4

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

7. Taylor expanded around inf 0.3

   \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{{r}^{2}} - 1.5\right)} - \frac{-2 \cdot v + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]

8. Simplified0.3

   \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} - 1.5\right)} - \frac{-2 \cdot v + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]
9. Using strategy rm

10. Applied div-inv0.4

    \[\leadsto \left(\frac{2}{r \cdot r} - 1.5\right) - \color{blue}{\left(\left(-2 \cdot v + 3\right) \cdot \frac{1}{1 - v}\right)} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]
11. Using strategy rm

12. Applied associate-/r*0.4

    \[\leadsto \left(\color{blue}{\frac{\frac{2}{r}}{r}} - 1.5\right) - \left(\left(-2 \cdot v + 3\right) \cdot \frac{1}{1 - v}\right) \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]

13. Final simplification0.4

    \[\leadsto \left(\frac{\frac{2}{r}}{r} - 1.5\right) - \left(\left(v \cdot -2 + 3\right) \cdot \frac{1}{1 - v}\right) \cdot \left(0.125 \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right)\]

Runtime

Time bar (total: 40.1s)Debug logProfile

herbie shell --seed 2018290 
(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))