\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
Test:
Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Time: 41.5 s
Input Error: 0.3
Output Error: 0.3
Log: ⚲
Profile: 🕒
\((\left(\sqrt[3]{\log \left(x + y\right)}\right) * \left(\sqrt[3]{\log \left(x + y\right) \cdot \log \left(x + y\right)}\right) + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right))_*\)
  1. Started with
    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
    0.3
  2. Applied simplify to get
    \[\color{red}{\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t} \leadsto \color{blue}{\log \left(x + y\right) + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right)}\]
    0.3
  3. Using strategy rm
    0.3
  4. Applied add-cbrt-cube to get
    \[\color{red}{\log \left(x + y\right)} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right) \leadsto \color{blue}{\sqrt[3]{{\left(\log \left(x + y\right)\right)}^3}} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right)\]
    0.3
  5. Using strategy rm
    0.3
  6. Applied cube-mult to get
    \[\sqrt[3]{\color{red}{{\left(\log \left(x + y\right)\right)}^3}} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right) \leadsto \sqrt[3]{\color{blue}{\log \left(x + y\right) \cdot \left(\log \left(x + y\right) \cdot \log \left(x + y\right)\right)}} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right)\]
    0.3
  7. Applied cbrt-prod to get
    \[\color{red}{\sqrt[3]{\log \left(x + y\right) \cdot \left(\log \left(x + y\right) \cdot \log \left(x + y\right)\right)}} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right) \leadsto \color{blue}{\sqrt[3]{\log \left(x + y\right)} \cdot \sqrt[3]{\log \left(x + y\right) \cdot \log \left(x + y\right)}} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right)\]
    0.3
  8. Applied fma-def to get
    \[\color{red}{\sqrt[3]{\log \left(x + y\right)} \cdot \sqrt[3]{\log \left(x + y\right) \cdot \log \left(x + y\right)} + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right)} \leadsto \color{blue}{(\left(\sqrt[3]{\log \left(x + y\right)}\right) * \left(\sqrt[3]{\log \left(x + y\right) \cdot \log \left(x + y\right)}\right) + \left((\left(a - 0.5\right) * \left(\log t\right) + \left(\log z\right))_* - t\right))_*}\]
    0.3
  9. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default))
  #:name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))