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. Taylor expanded around inf 0.3

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

4. Simplified0.3

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

6. Applied add-cube-cbrt0.8

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

7. Applied add-sqr-sqrt32.0

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

8. Applied prod-diff32.0

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

9. Simplified0.3

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

10. Simplified0.3

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

12. Applied add-sqr-sqrt0.3

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

13. Applied log-prod0.3

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

14. Applied associate-+l+0.3

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

15. Final simplification0.3

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

Runtime

Time bar (total: 46.9s)Debug logProfile

herbie shell --seed 2018353 +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))))