Average Error: 28.9 → 28.9
Time: 1.2m
Precision: 64
Internal Precision: 320
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{(y \cdot \left((\left(a + y\right) \cdot \left(y \cdot y\right) + \left((y \cdot b + c)_*\right))_*\right) + i)_*} \cdot (y \cdot \left((\left((y \cdot x + z)_*\right) \cdot \left(y \cdot y\right) + \left((y \cdot 27464.7644705 + 230661.510616)_*\right))_*\right) + t)_*\]

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 28.9

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

  3. Applied div-inv28.9

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

  5. Applied pow128.9

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

  6. Applied pow128.9

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

  7. Applied pow-prod-down28.9

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

  8. Simplified28.9

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

  10. Applied div-inv28.9

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

  11. Final simplification28.9

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018235 +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)))