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

⬇

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

Error

The X axis uses an exponential scale — Bits error versus `v`

Derivation

Initial program 12.3
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Applied simplify 0.4
\[\leadsto \color{blue}{\left(\frac{\frac{2}{r}}{r} + \left(3 - 4.5\right)\right) - \frac{0.125 \cdot {\left(w \cdot r\right)}^2}{\frac{1 - v}{\left(3 - v\right) - v}}}\]
Applied taylor 0.4
\[\leadsto \left(\frac{2}{{r}^2} + \left(3 - 4.5\right)\right) - \frac{0.125 \cdot {\left(w \cdot r\right)}^2}{\frac{1 - v}{\left(3 - v\right) - v}}\]
Taylor expanded around 0 0.4

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

Runtime

Please include this information when filing a bug report:

herbie --seed '#(1046999656 3709967244 1006838154 1022019954 4151880389 758329559)'
(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))