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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 *-un-lft-identity0.4

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

5. Applied associate-/l*0.4

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

7. Applied associate-/r*0.4

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

8. Final simplification0.4

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018263 
(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))