Average Error: 29.2 → 29.3
Time: 8.2s
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 r61868 = x;
        double r61869 = y;
        double r61870 = r61868 * r61869;
        double r61871 = z;
        double r61872 = r61870 + r61871;
        double r61873 = r61872 * r61869;
        double r61874 = 27464.7644705;
        double r61875 = r61873 + r61874;
        double r61876 = r61875 * r61869;
        double r61877 = 230661.510616;
        double r61878 = r61876 + r61877;
        double r61879 = r61878 * r61869;
        double r61880 = t;
        double r61881 = r61879 + r61880;
        double r61882 = a;
        double r61883 = r61869 + r61882;
        double r61884 = r61883 * r61869;
        double r61885 = b;
        double r61886 = r61884 + r61885;
        double r61887 = r61886 * r61869;
        double r61888 = c;
        double r61889 = r61887 + r61888;
        double r61890 = r61889 * r61869;
        double r61891 = i;
        double r61892 = r61890 + r61891;
        double r61893 = r61881 / r61892;
        return r61893;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61894 = x;
        double r61895 = y;
        double r61896 = r61894 * r61895;
        double r61897 = z;
        double r61898 = r61896 + r61897;
        double r61899 = r61898 * r61895;
        double r61900 = 27464.7644705;
        double r61901 = r61899 + r61900;
        double r61902 = r61901 * r61895;
        double r61903 = 230661.510616;
        double r61904 = r61902 + r61903;
        double r61905 = r61904 * r61895;
        double r61906 = t;
        double r61907 = r61905 + r61906;
        double r61908 = 1.0;
        double r61909 = a;
        double r61910 = r61895 + r61909;
        double r61911 = r61910 * r61895;
        double r61912 = b;
        double r61913 = r61911 + r61912;
        double r61914 = r61913 * r61895;
        double r61915 = c;
        double r61916 = r61914 + r61915;
        double r61917 = r61916 * r61895;
        double r61918 = i;
        double r61919 = r61917 + r61918;
        double r61920 = r61908 / r61919;
        double r61921 = r61907 * r61920;
        return r61921;
}

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 29.2

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

  3. Applied div-inv29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2020025 
(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)))