Average Error: 29.3 → 29.9
Time: 13.0s
Precision: binary64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \left(\sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}} \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right)\right) \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\]
\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}
↓
\left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \left(\sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}} \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right)\right) \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) + z)) * y)) + 27464.7644705)) * y)) + 230661.510616)) * y)) + t)) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (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 ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) + z)) * y)) + 27464.7644705)) * y)) + 230661.510616)) * y)) + t)) * ((double) (((double) cbrt((1.0 / ((double) (((double) (((double) (((double) (((double) pow(y, 2.0)) * ((double) (y + a)))) + ((double) (((double) (y * b)) + c)))) * y)) + i))))) * ((double) cbrt((1.0 / ((double) (((double) (((double) (((double) (((double) pow(y, 2.0)) * ((double) (y + a)))) + ((double) (((double) (y * b)) + c)))) * y)) + i))))))))) * ((double) cbrt((1.0 / ((double) (((double) (((double) (((double) (((double) pow(y, 2.0)) * ((double) (y + a)))) + ((double) (((double) (y * b)) + 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 29.3

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

  2. Taylor expanded around inf 29.4

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(a \cdot {y}^{2} + \left(y \cdot b + {y}^{3}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied div-inv29.4

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(a \cdot {y}^{2} + \left(y \cdot b + {y}^{3}\right)\right) + c\right) \cdot y + i}}\]

  5. Simplified29.4

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt29.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}} \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right) \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right)}\]

  8. Applied associate-*r*29.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \left(\sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}} \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right)\right) \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}}\]

  9. Final simplification29.9

    \[\leadsto \left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \left(\sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}} \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\right)\right) \cdot \sqrt[3]{\frac{1}{\left({y}^{2} \cdot \left(y + a\right) + \left(y \cdot b + c\right)\right) \cdot y + i}}\]

Reproduce

herbie shell --seed 2020182 
(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)))