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

↓

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

Error

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

Derivation

Initial program 12.1
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Applied simplify0.4
\[\leadsto \color{blue}{\left(\frac{\frac{2}{r}}{r} + 3\right) - (\left(\frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*}\]
Using strategy rm
Applied expm1-log1p-u0.4
\[\leadsto \left(\frac{\frac{2}{r}}{r} + 3\right) - (\color{blue}{\left((e^{\log_* (1 + \frac{3 - v \cdot 2}{\frac{1 - v}{0.125}})} - 1)^*\right)} \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]

Runtime

herbie shell --seed 2018207 +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))