Error

Derivation

1. Initial program 12.1

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

2. Simplified0.4

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

4. Applied associate-/r/0.4

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

5. Taylor expanded around -inf 0.3

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

6. Simplified0.3

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

8. Applied add-cbrt-cube0.4

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

9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019089 
(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))