\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Test:
Rosa's TurbineBenchmark
Bits:
128 bits
Bits error versus v
Bits error versus w
Bits error versus r
Time: 19.0 s
Input Error: 12.5
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{3 - 2 \cdot v}}\)
  1. Started with
    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    12.5
  2. Applied simplify to get
    \[\color{red}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5} \leadsto \color{blue}{\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(w \cdot r\right)}^2}\]
    0.4
  3. Applied taylor to get
    \[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(w \cdot r\right)}^2 \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)\]
    17.4
  4. Taylor expanded around inf to get
    \[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{red}{\left({w}^2 \cdot {r}^2\right)} \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left({w}^2 \cdot {r}^2\right)}\]
    17.4
  5. Applied simplify to get
    \[\color{red}{\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)} \leadsto \color{blue}{\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{3 - 2 \cdot v}}}\]
    0.4
  6. Removed slow pow expressions

Original test:


(lambda ((v default) (w default) (r default))
  #:name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))