\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Test:
Rosa's TurbineBenchmark
Bits:
128 bits
Bits error versus v
Bits error versus w
Bits error versus r
Time: 17.8 s
Input Error: 5.9
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(\frac{2}{r \cdot r} + 3\right) - \left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot {\left(\left|r \cdot w\right|\right)}^2 + 4.5\right)\)
  1. Started with
    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    5.9
  2. Applied simplify to get
    \[\color{red}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5} \leadsto \color{blue}{\left(\frac{2}{r \cdot r} + 3\right) - (\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) * \left({\left(w \cdot r\right)}^2\right) + 4.5)_*}\]
    0.6
  3. Using strategy rm
    0.6
  4. Applied fma-udef to get
    \[\left(\frac{2}{r \cdot r} + 3\right) - \color{red}{(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) * \left({\left(w \cdot r\right)}^2\right) + 4.5)_*} \leadsto \left(\frac{2}{r \cdot r} + 3\right) - \color{blue}{\left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot {\left(w \cdot r\right)}^2 + 4.5\right)}\]
    0.6
  5. Using strategy rm
    0.6
  6. Applied add-sqr-sqrt to get
    \[\left(\frac{2}{r \cdot r} + 3\right) - \left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot \color{red}{{\left(w \cdot r\right)}^2} + 4.5\right) \leadsto \left(\frac{2}{r \cdot r} + 3\right) - \left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot \color{blue}{{\left(\sqrt{{\left(w \cdot r\right)}^2}\right)}^2} + 4.5\right)\]
    0.6
  7. Applied simplify to get
    \[\left(\frac{2}{r \cdot r} + 3\right) - \left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot {\color{red}{\left(\sqrt{{\left(w \cdot r\right)}^2}\right)}}^2 + 4.5\right) \leadsto \left(\frac{2}{r \cdot r} + 3\right) - \left(\left(\left(3 - 2 \cdot v\right) \cdot \frac{0.125}{1 - v}\right) \cdot {\color{blue}{\left(\left|r \cdot w\right|\right)}}^2 + 4.5\right)\]
    0.4
  8. 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))