Error

Derivation

1. Initial program 60.9

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

2. Initial simplification60.2

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

3. Taylor expanded around 0 59.8

   \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - (\color{blue}{\left(0.125 \cdot {v}^{2} + \left(0.125 \cdot v + 0.375\right)\right)} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]

4. Simplified59.8

   \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - (\color{blue}{\left((v \cdot \left((v \cdot 0.125 + 0.125)_*\right) + 0.375)_*\right)} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]
5. Using strategy rm

6. Applied associate-*l*59.8

   \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - (\left((v \cdot \left((v \cdot 0.125 + 0.125)_*\right) + 0.375)_*\right) \cdot \color{blue}{\left(w \cdot \left(r \cdot \left(w \cdot r\right)\right)\right)} + 4.5)_*\]

7. Final simplification59.8

   \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - (\left((v \cdot \left((v \cdot 0.125 + 0.125)_*\right) + 0.375)_*\right) \cdot \left(w \cdot \left(r \cdot \left(w \cdot r\right)\right)\right) + 4.5)_*\]

Runtime

Time bar (total: 37.9s)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))