\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
Test:
Octave 3.8, jcobi/3
Bits:
128 bits
Bits error versus alpha
Bits error versus beta
Time: 39.8 s
Input Error: 3.6
Output Error: 4.7
Log:
Profile: 🕒
\(\frac{\sqrt[3]{{\left(\frac{(\beta * \alpha + \beta)_* + \left(\alpha + 1.0\right)}{2 + \left(\beta + \alpha\right)}\right)}^3}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\)
  1. Started with
    \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
    3.6
  2. Applied simplify to get
    \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
    4.5
  3. Using strategy rm
    4.5
  4. Applied add-cbrt-cube to get
    \[\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\color{red}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\color{blue}{\sqrt[3]{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
    9.9
  5. Applied add-cbrt-cube to get
    \[\frac{\frac{\color{red}{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}}{\sqrt[3]{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\color{blue}{\sqrt[3]{{\left(\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*\right)}^3}}}{\sqrt[3]{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
    25.9
  6. Applied cbrt-undiv to get
    \[\frac{\color{red}{\frac{\sqrt[3]{{\left(\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*\right)}^3}}{\sqrt[3]{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{\sqrt[3]{\frac{{\left(\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*\right)}^3}{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
    25.9
  7. Applied simplify to get
    \[\frac{\sqrt[3]{\color{red}{\frac{{\left(\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*\right)}^3}{{\left(\alpha + \left(2 + \beta\right)\right)}^3}}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\sqrt[3]{\color{blue}{{\left(\frac{(\beta * \alpha + \beta)_* + \left(\alpha + 1.0\right)}{2 + \left(\beta + \alpha\right)}\right)}^3}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
    4.7

Original test:


(lambda ((alpha default) (beta default))
  #:name "Octave 3.8, jcobi/3"
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))