Average Error: 28.1 → 28.3
Time: 2.8m
Precision: 64
Internal Precision: 320
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{(\left((\left(y \cdot y\right) \cdot \left(a + y\right) + \left((y \cdot b + c)_*\right))_*\right) \cdot y + i)_*}{(\left((\left((x \cdot y + z)_*\right) \cdot y + 27464.7644705)_*\right) \cdot \left(y \cdot y\right) + \left((y \cdot 230661.510616 + t)_*\right))_*}}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

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 clear-num28.3

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

  4. Applied simplify28.3

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

Runtime

Time bar (total: 2.8m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +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)))