Average Error: 28.7 → 28.8
Time: 1.7m
Precision: 64
Internal Precision: 576
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(230661.510616 \cdot y + t\right) + 27464.7644705 \cdot \left(y \cdot y\right)\right) + y \cdot \left(\left(x \cdot y + z\right) \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot b\right) + \left(\left(i + c \cdot y\right) + {y}^{3} \cdot \left(a + y\right)\right)}\]

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-cbrt28.7

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

  5. Applied *-un-lft-identity28.7

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

  6. Applied *-un-lft-identity28.7

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

  7. Applied times-frac28.7

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

  8. Simplified28.7

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

  9. Simplified28.8

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

  10. Final simplification28.8

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed 2018248 
(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)))