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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 associate-/r/0.4

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

6. Applied associate-/r*0.4

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

8. Applied associate-*r*0.3

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

10. Applied associate-*r*0.3

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

11. Final simplification0.3

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

Runtime

Time bar (total: 40.9s)Debug logProfile

herbie shell --seed 2018274 
(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))