Average Error: 61.0 → 58.2
Time: 1.2m
Precision: 64
Internal Precision: 128
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\log \left(e^{\sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)} \cdot \sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}\right) \cdot \sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}\right) \cdot \frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}\]

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

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.0

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

  3. Applied add-log-exp60.6

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

  5. Applied div-inv60.6

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

  6. Applied exp-prod58.3

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

  7. Applied log-pow58.3

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

  9. Applied add-cube-cbrt58.3

    \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \log \left(e^{\color{blue}{\left(\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t} \cdot \sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right) \cdot \sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\right)\]

  10. Applied exp-prod58.3

    \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \log \color{blue}{\left({\left(e^{\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t} \cdot \sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\right)}^{\left(\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}\right)}\]

  11. Applied log-pow58.2

    \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t} \cdot \log \left(e^{\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t} \cdot \sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\right)\right)}\]

  12. Final simplification58.2

    \[\leadsto \left(\log \left(e^{\sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)} \cdot \sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}}\right) \cdot \sqrt[3]{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)}\right) \cdot \frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018255 
(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)))