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Derivation

1. Initial program 0.3

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

2. Initial simplification0.3

   \[\leadsto \left(\log \left(y + x\right) + \left(a - 0.5\right) \cdot \log t\right) - \left(t - \log z\right)\]
3. Using strategy rm

4. Applied add-cube-cbrt0.7

   \[\leadsto \left(\log \left(y + x\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\log t} \cdot \sqrt[3]{\log t}\right) \cdot \sqrt[3]{\log t}\right)}\right) - \left(t - \log z\right)\]

5. Applied associate-*r*0.7

   \[\leadsto \left(\log \left(y + x\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \left(\sqrt[3]{\log t} \cdot \sqrt[3]{\log t}\right)\right) \cdot \sqrt[3]{\log t}}\right) - \left(t - \log z\right)\]

6. Taylor expanded around -inf 62.8

   \[\leadsto \left(\log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \color{blue}{{\left({\left(\log -1 - \log \left(\frac{-1}{t}\right)\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\log t}\right) - \left(t - \log z\right)\]

7. Simplified0.5

   \[\leadsto \left(\log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \color{blue}{\sqrt[3]{\log t \cdot \log t}}\right) \cdot \sqrt[3]{\log t}\right) - \left(t - \log z\right)\]

8. Final simplification0.5

   \[\leadsto \left(\log \left(x + y\right) + \left(\sqrt[3]{\log t \cdot \log t} \cdot \left(a - 0.5\right)\right) \cdot \sqrt[3]{\log t}\right) - \left(t - \log z\right)\]

Runtime

Time bar (total: 50.5s)Debug logProfile

herbie shell --seed 2018274 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))