Average Error: 29.5 → 29.5
Time: 15.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\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(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80791 = x;
        double r80792 = y;
        double r80793 = r80791 * r80792;
        double r80794 = z;
        double r80795 = r80793 + r80794;
        double r80796 = r80795 * r80792;
        double r80797 = 27464.7644705;
        double r80798 = r80796 + r80797;
        double r80799 = r80798 * r80792;
        double r80800 = 230661.510616;
        double r80801 = r80799 + r80800;
        double r80802 = r80801 * r80792;
        double r80803 = t;
        double r80804 = r80802 + r80803;
        double r80805 = a;
        double r80806 = r80792 + r80805;
        double r80807 = r80806 * r80792;
        double r80808 = b;
        double r80809 = r80807 + r80808;
        double r80810 = r80809 * r80792;
        double r80811 = c;
        double r80812 = r80810 + r80811;
        double r80813 = r80812 * r80792;
        double r80814 = i;
        double r80815 = r80813 + r80814;
        double r80816 = r80804 / r80815;
        return r80816;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80817 = x;
        double r80818 = y;
        double r80819 = r80817 * r80818;
        double r80820 = z;
        double r80821 = r80819 + r80820;
        double r80822 = r80821 * r80818;
        double r80823 = 27464.7644705;
        double r80824 = r80822 + r80823;
        double r80825 = r80824 * r80818;
        double r80826 = 230661.510616;
        double r80827 = r80825 + r80826;
        double r80828 = r80827 * r80818;
        double r80829 = t;
        double r80830 = r80828 + r80829;
        double r80831 = b;
        double r80832 = r80818 * r80831;
        double r80833 = 3.0;
        double r80834 = pow(r80818, r80833);
        double r80835 = a;
        double r80836 = 2.0;
        double r80837 = pow(r80818, r80836);
        double r80838 = r80835 * r80837;
        double r80839 = r80834 + r80838;
        double r80840 = r80832 + r80839;
        double r80841 = c;
        double r80842 = r80840 + r80841;
        double r80843 = r80842 * r80818;
        double r80844 = i;
        double r80845 = r80843 + r80844;
        double r80846 = r80830 / r80845;
        return r80846;
}

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 29.5

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

  2. Taylor expanded around inf 29.5

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

  3. Final simplification29.5

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

Reproduce

herbie shell --seed 2020046 
(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)))