Error

Derivation

1. Initial program 11.8

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

2. Initial simplification0.4

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

4. Applied associate-/r*0.4

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

6. Applied fma-udef0.4

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

8. Applied add-cbrt-cube0.5

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

9. Final simplification0.5

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(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))