Average Error: 29.0 → 29.0
Time: 7.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(t + y \cdot \left(y \cdot {\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right)}^{3} + y \cdot 27464.764470499998\right)\right) + y \cdot 230661.510616000014}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(t + y \cdot \left(y \cdot {\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right)}^{3} + y \cdot 27464.764470499998\right)\right) + y \cdot 230661.510616000014}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((t + (y * ((y * pow(cbrt((((x * y) + z) * y)), 3.0)) + (y * 27464.7644705)))) + (y * 230661.510616)) / (((((((y + a) * y) + b) * y) + c) * y) + i));
}

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 29.0

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.0

    \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity29.0

    \[\leadsto \frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\color{blue}{1 \cdot \left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}}\]

  6. Applied associate-/r*29.0

    \[\leadsto \color{blue}{\frac{\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{1}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  7. Simplified29.0

    \[\leadsto \frac{\color{blue}{\left(t + y \cdot \left(y \cdot {\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right)}^{3} + y \cdot 27464.764470499998\right)\right) + y \cdot 230661.510616000014}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  8. Final simplification29.0

    \[\leadsto \frac{\left(t + y \cdot \left(y \cdot {\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right)}^{3} + y \cdot 27464.764470499998\right)\right) + y \cdot 230661.510616000014}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))