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Derivation

1. Initial program 27.9

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

2. Taylor expanded around 0 27.9

   \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot {y}^{2} + z \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

3. Simplified27.9

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

4. Final simplification27.9

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018351 
(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)))