Average Error: 28.7 → 28.8
Time: 1.6m
Precision: 64
Internal Precision: 128
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(\left(\sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*} \cdot \sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*}\right) \cdot \left(\sqrt[3]{\left(y \cdot x + z\right) \cdot y + 27464.7644705} \cdot y\right) + 230661.510616\right) + t}{i + \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right) \cdot y}\]

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 28.7

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

  3. Applied add-cube-cbrt28.8

    \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705}\right)} \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.8

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705} \cdot y\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  5. Simplified28.8

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*} \cdot \sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*}\right)} \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644705} \cdot y\right) + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  6. Final simplification28.8

    \[\leadsto \frac{y \cdot \left(\left(\sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*} \cdot \sqrt[3]{(y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*}\right) \cdot \left(\sqrt[3]{\left(y \cdot x + z\right) \cdot y + 27464.7644705} \cdot y\right) + 230661.510616\right) + t}{i + \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right) \cdot y}\]

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018274 +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)))