Error

Derivation

1. Initial program 28.2

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
2. Using strategy rm

3. Applied *-un-lft-identity28.2

   \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-/l*28.4

   \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
5. Using strategy rm

6. Applied associate-/r/28.3

   \[\leadsto \color{blue}{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}\]

7. Simplified28.3

   \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{(\left(y \cdot y\right) \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + \left((y \cdot 230661.510616 + t)_*\right))_*}\]

8. Final simplification28.3

   \[\leadsto (\left(y \cdot y\right) \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + \left((y \cdot 230661.510616 + t)_*\right))_* \cdot \frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

Details

Time bar (total: 58.6s)Debug log