Average Error: 28.8 → 28.9
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}}{\frac{1}{(y \cdot \left((\left((y \cdot x + z)_*\right) \cdot \left(y \cdot y\right) + \left((27464.7644705 \cdot y + 230661.510616)_*\right))_*\right) + t)_*}}\]

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 28.8

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

  3. Applied clear-num29.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  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*28.9

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

  7. Simplified28.9

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

  8. Final simplification28.9

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed 2018217 +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)))