\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Test:
Rosa's TurbineBenchmark
Bits:
128 bits
Bits error versus v
Bits error versus w
Bits error versus r
Time: 21.6 s
Input Error: 12.3
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\left(\left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot w\right) \cdot r\right) \cdot \left(w \cdot r\right)\)
  1. Started with
    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
    12.3
  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. Using strategy rm
    0.4
  4. Applied square-mult to get
    \[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{red}{{\left(w \cdot r\right)}^2} \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)}\]
    0.4
  5. Applied associate-*r* to get
    \[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \color{red}{\left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)} \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(w \cdot r\right)\right) \cdot \left(w \cdot r\right)}\]
    0.3
  6. Using strategy rm
    0.3
  7. Applied associate-*r* to get
    \[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \color{red}{\left(\left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(w \cdot r\right)\right)} \cdot \left(w \cdot r\right) \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\left(\left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot w\right) \cdot r\right)} \cdot \left(w \cdot r\right)\]
    0.3
  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))