Error

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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. Simplified0.2

   \[\leadsto \color{blue}{\log \left(y + x\right) + \left((\left(a - 0.5\right) \cdot \left(\log t\right) + \left(\log z\right))_* - t\right)}\]
3. Using strategy rm

4. Applied fma-udef0.2

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

5. Applied associate--l+0.2

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

6. Applied associate-+r+0.3

   \[\leadsto \color{blue}{\left(\log \left(y + x\right) + \left(a - 0.5\right) \cdot \log t\right) + \left(\log z - t\right)}\]
7. Using strategy rm

8. Applied associate-+l+0.2

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

9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(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))))

Details

Time bar (total: 43.9s)Debug log