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

↓

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

Error

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

Derivation

Initial program 0.3
\[\left(\left(3 - \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(1 + 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 0.5\]
Using strategy rm
Applied *-un-lft-identity0.3
\[\leadsto \left(\left(3 - \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(1 + 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 0.5\]
Applied times-frac0.3
\[\leadsto \left(\left(3 - \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(1 + 2 \cdot v\right)}{1} \cdot \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}{1 - v}}\right) - 0.5\]

Runtime

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(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))