Error

Derivation

1. Initial program 28.1

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

3. Applied *-un-lft-identity28.1

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

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 div-inv28.4

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

7. Applied associate-/r*28.2

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

8. Simplified28.2

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

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

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

11. Applied associate-/r*28.2

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

12. Simplified28.3

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

14. Applied associate-/l/28.4

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

15. Simplified28.4

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

16. Final simplification28.4

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed 2018340 +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)))