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

↓

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

Derivation

Initial program 12.8
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Using strategy rm
Applied *-un-lft-identity12.8
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 4.5\]
Applied times-frac8.8
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1} \cdot \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}{1 - v}}\right) - 4.5\]
Taylor expanded around inf 17.2
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1} \cdot \frac{\color{blue}{{w}^{2} \cdot {r}^{2}}}{1 - v}\right) - 4.5\]
Applied simplify0.3
\[\leadsto \color{blue}{\left(\frac{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \left(0.125 \cdot \left(\left(3 - v\right) - v\right)\right) \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}\]

Runtime

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' 
(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))

Error

Derivation

Runtime