Error

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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. Taylor expanded around -inf 20.9

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\color{blue}{0.375 \cdot \left({r}^{2} \cdot {w}^{2}\right) - 0.25 \cdot \left({r}^{2} \cdot \left(v \cdot {w}^{2}\right)\right)}}{1 - v}\right) - 4.5\]

3. Simplified6.1

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\color{blue}{\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \left(v \cdot \left(-0.25\right) + 0.375\right)}}{1 - v}\right) - 4.5\]
4. Using strategy rm

5. Applied *-un-lft-identity6.1

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \left(v \cdot \left(-0.25\right) + 0.375\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 4.5\]

6. Applied times-frac0.3

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{1} \cdot \frac{v \cdot \left(-0.25\right) + 0.375}{1 - v}}\right) - 4.5\]

7. Simplified0.3

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)} \cdot \frac{v \cdot \left(-0.25\right) + 0.375}{1 - v}\right) - 4.5\]

8. Simplified0.3

   \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \color{blue}{\frac{0.375 - v \cdot 0.25}{1 - v}}\right) - 4.5\]
9. Using strategy rm

10. Applied associate-/r*0.3

    \[\leadsto \left(\left(3 + \color{blue}{\frac{\frac{2}{r}}{r}}\right) - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \frac{0.375 - v \cdot 0.25}{1 - v}\right) - 4.5\]
11. Using strategy rm

12. Applied add-sqr-sqrt0.4

    \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \color{blue}{\sqrt{\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \frac{0.375 - v \cdot 0.25}{1 - v}} \cdot \sqrt{\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \frac{0.375 - v \cdot 0.25}{1 - v}}}\right) - 4.5\]

13. Final simplification0.4

    \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \sqrt{\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \frac{0.375 - v \cdot 0.25}{1 - v}} \cdot \sqrt{\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \frac{0.375 - v \cdot 0.25}{1 - v}}\right) - 4.5\]

Reproduce

herbie shell --seed 2019002 
(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))

Details

Time bar (total: 37.5s)Debug log