Average Error: 28.9 → 28.9
Time: 8.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\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(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r96788 = x;
        double r96789 = y;
        double r96790 = r96788 * r96789;
        double r96791 = z;
        double r96792 = r96790 + r96791;
        double r96793 = r96792 * r96789;
        double r96794 = 27464.7644705;
        double r96795 = r96793 + r96794;
        double r96796 = r96795 * r96789;
        double r96797 = 230661.510616;
        double r96798 = r96796 + r96797;
        double r96799 = r96798 * r96789;
        double r96800 = t;
        double r96801 = r96799 + r96800;
        double r96802 = a;
        double r96803 = r96789 + r96802;
        double r96804 = r96803 * r96789;
        double r96805 = b;
        double r96806 = r96804 + r96805;
        double r96807 = r96806 * r96789;
        double r96808 = c;
        double r96809 = r96807 + r96808;
        double r96810 = r96809 * r96789;
        double r96811 = i;
        double r96812 = r96810 + r96811;
        double r96813 = r96801 / r96812;
        return r96813;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r96814 = x;
        double r96815 = y;
        double r96816 = r96814 * r96815;
        double r96817 = z;
        double r96818 = r96816 + r96817;
        double r96819 = r96818 * r96815;
        double r96820 = 27464.7644705;
        double r96821 = r96819 + r96820;
        double r96822 = r96821 * r96815;
        double r96823 = 230661.510616;
        double r96824 = r96822 + r96823;
        double r96825 = r96824 * r96815;
        double r96826 = t;
        double r96827 = r96825 + r96826;
        double r96828 = 1.0;
        double r96829 = a;
        double r96830 = r96815 + r96829;
        double r96831 = r96830 * r96815;
        double r96832 = b;
        double r96833 = r96831 + r96832;
        double r96834 = r96833 * r96815;
        double r96835 = c;
        double r96836 = r96834 + r96835;
        double r96837 = r96836 * r96815;
        double r96838 = i;
        double r96839 = r96837 + r96838;
        double r96840 = r96828 / r96839;
        double r96841 = r96827 * r96840;
        return r96841;
}

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 28.9

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

  3. Applied div-inv28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2020021 
(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)))