\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Test:
Rosa's TurbineBenchmark
Bits:
128 bits
Bits error versus v
Bits error versus w
Bits error versus r
Time: 18.3 s
Input Error: 12.5
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(\frac{2}{r \cdot r} + 3\right) - (\left(\frac{3 - 2 \cdot v}{\frac{1 - v}{0.125}}\right) * \left({\left(r \cdot w\right)}^2\right) + 4.5)_*\)
  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
    \[\color{red}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5} \leadsto \color{blue}{\left(\frac{2}{r \cdot r} + 3\right) - (\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) * \left({\left(w \cdot r\right)}^2\right) + 4.5)_*}\]
    0.4
  3. Applied taylor to get
    \[\left(\frac{2}{r \cdot r} + 3\right) - (\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) * \left({\left(w \cdot r\right)}^2\right) + 4.5)_* \leadsto \left(3 + 2 \cdot \frac{1}{{r}^2}\right) - (\left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right) * \left({w}^2 \cdot {r}^2\right) + 4.5)_*\]
    17.1
  4. Taylor expanded around 0 to get
    \[\color{red}{\left(3 + 2 \cdot \frac{1}{{r}^2}\right) - (\left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right) * \left({w}^2 \cdot {r}^2\right) + 4.5)_*} \leadsto \color{blue}{\left(3 + 2 \cdot \frac{1}{{r}^2}\right) - (\left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right) * \left({w}^2 \cdot {r}^2\right) + 4.5)_*}\]
    17.1
  5. Applied simplify to get
    \[\color{red}{\left(3 + 2 \cdot \frac{1}{{r}^2}\right) - (\left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right) * \left({w}^2 \cdot {r}^2\right) + 4.5)_*} \leadsto \color{blue}{\left(\frac{2}{r \cdot r} + 3\right) - (\left(\frac{3 - 2 \cdot v}{\frac{1 - v}{0.125}}\right) * \left({\left(r \cdot w\right)}^2\right) + 4.5)_*}\]
    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))