Average Error: 28.7 → 28.9
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{i + y \cdot \left(c + y \cdot \left(\left(a + y\right) \cdot y + b\right)\right)} \cdot \left(y \cdot \left(230661.510616 + \left(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705}\right) \cdot \left(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot y\right)\right) + t\right)\]

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

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  6. Applied div-inv28.9

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

  7. Final simplification28.9

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018254 
(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)))