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. Applied simplify0.3

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

4. Applied add-cube-cbrt1.3

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

5. Applied pow11.3

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

6. Applied log-pow1.3

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

7. Applied prod-diff1.3

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

8. Applied simplify0.3

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

9. Applied simplify0.3

   \[\leadsto \left(\left(\log \left(y + x\right) - (\left(0.5 - a\right) \cdot \left(\log t\right) + t)_*\right) + \log z\right) + \color{blue}{0}\]

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed 2018207 +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))))