Error

Derivation

1. Initial program 28.7

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

3. Applied clear-num28.9

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

5. Applied div-inv29.0

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

6. Applied associate-/r*28.8

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

7. Simplified28.8

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

9. Applied associate-/r/28.8

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

10. Final simplification28.8

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

Reproduce

herbie shell --seed 2019008 +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: 1.1m)Debug log