Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 9.6s

Precision: 64

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61851 = x;
        double r61852 = y;
        double r61853 = r61851 * r61852;
        double r61854 = z;
        double r61855 = r61853 + r61854;
        double r61856 = r61855 * r61852;
        double r61857 = 27464.7644705;
        double r61858 = r61856 + r61857;
        double r61859 = r61858 * r61852;
        double r61860 = 230661.510616;
        double r61861 = r61859 + r61860;
        double r61862 = r61861 * r61852;
        double r61863 = t;
        double r61864 = r61862 + r61863;
        double r61865 = a;
        double r61866 = r61852 + r61865;
        double r61867 = r61866 * r61852;
        double r61868 = b;
        double r61869 = r61867 + r61868;
        double r61870 = r61869 * r61852;
        double r61871 = c;
        double r61872 = r61870 + r61871;
        double r61873 = r61872 * r61852;
        double r61874 = i;
        double r61875 = r61873 + r61874;
        double r61876 = r61864 / r61875;
        return r61876;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61877 = x;
        double r61878 = y;
        double r61879 = r61877 * r61878;
        double r61880 = z;
        double r61881 = r61879 + r61880;
        double r61882 = r61881 * r61878;
        double r61883 = 27464.7644705;
        double r61884 = r61882 + r61883;
        double r61885 = cbrt(r61884);
        double r61886 = r61885 * r61885;
        double r61887 = r61885 * r61878;
        double r61888 = r61886 * r61887;
        double r61889 = 230661.510616;
        double r61890 = r61888 + r61889;
        double r61891 = r61890 * r61878;
        double r61892 = t;
        double r61893 = r61891 + r61892;
        double r61894 = a;
        double r61895 = r61878 + r61894;
        double r61896 = r61895 * r61878;
        double r61897 = b;
        double r61898 = r61896 + r61897;
        double r61899 = r61898 * r61878;
        double r61900 = c;
        double r61901 = r61899 + r61900;
        double r61902 = r61901 * r61878;
        double r61903 = i;
        double r61904 = r61902 + r61903;
        double r61905 = r61893 / r61904;
        return r61905;
}

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

Derivation

1. Initial program 29.1

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
2. Using strategy rm

3. Applied add-cube-cbrt 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right)} \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-*l* 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

5. Final simplification 29.2

   \[\leadsto \frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019362 +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)))