Error

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

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

4. Applied associate-+r-0.2

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

6. Applied add-cube-cbrt0.2

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

7. Applied log-prod0.3

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

8. Applied associate-+l+0.3

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

9. Final simplification0.3

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018230 +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))))