Error

Derivation

1. Initial program 0.3

   \[\left(\left(3 - \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(1 + 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 0.5\]

2. Applied simplify 0.3

   \[\leadsto \color{blue}{\left(3 - \frac{\frac{2}{r}}{r}\right) - \left(\frac{{\left(r \cdot w\right)}^2 \cdot \left(\left(v + v\right) + 1\right)}{\frac{1 - v}{0.125}} + 0.5\right)}\]

3. Applied taylor 0.3

   \[\leadsto \left(3 - \frac{\frac{2}{r}}{r}\right) - \left(\frac{2 \cdot \left(v \cdot \left({w}^2 \cdot {r}^2\right)\right) + {w}^2 \cdot {r}^2}{\frac{1 - v}{0.125}} + 0.5\right)\]

4. Taylor expanded around inf 0.3

   \[\leadsto \left(3 - \frac{\frac{2}{r}}{r}\right) - \left(\frac{\color{blue}{2 \cdot \left(v \cdot \left({w}^2 \cdot {r}^2\right)\right) + {w}^2 \cdot {r}^2}}{\frac{1 - v}{0.125}} + 0.5\right)\]

5. Applied simplify 0.2

   \[\leadsto \color{blue}{3 - \left(\left(0.5 + \frac{2}{r \cdot r}\right) + \frac{\left(1 + \left(v + v\right)\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)}{\frac{1 - v}{0.125}}\right)}\]

6. Applied taylor 0.2

   \[\leadsto 3 - \left(\left(0.5 + \frac{2}{r \cdot r}\right) + \frac{\left(1 + \left(v + v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)}{\frac{1 - v}{0.125}}\right)\]

7. Taylor expanded around inf 0.2

   \[\leadsto 3 - \left(\left(0.5 + \frac{2}{r \cdot r}\right) + \frac{\left(1 + \left(v + v\right)\right) \cdot \color{blue}{\left({w}^2 \cdot {r}^2\right)}}{\frac{1 - v}{0.125}}\right)\]
8. Removed slow pow expressions

Runtime

Time bar (total: 43.2s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (v w r)
  :name "turbine3"
  :pre (and (<= -4.5 v -0.3) (<= 0.4 w 0.9) (<= 3.8 r 7.8))
  (- (- (- 3 (/ 2 (* r r))) (/ (* (* 0.125 (+ 1 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 0.5))