Average Error: 28.6 → 28.9
Time: 2.6m
Precision: 64
Internal Precision: 576
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{(\left((\left(y \cdot y\right) \cdot \left(a + y\right) + \left((y \cdot b + c)_*\right))_*\right) \cdot y + i)_*}{(\left((\left((x \cdot y + z)_*\right) \cdot y + 27464.7644705)_*\right) \cdot \left(y \cdot y\right) + \left((y \cdot 230661.510616 + t)_*\right))_*}}\]

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

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 28.6

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

  3. Applied clear-num28.9

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

  4. Applied simplify28.9

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

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +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)))