Average Error: 29.2 → 29.3
Time: 15.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\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(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62873 = x;
        double r62874 = y;
        double r62875 = r62873 * r62874;
        double r62876 = z;
        double r62877 = r62875 + r62876;
        double r62878 = r62877 * r62874;
        double r62879 = 27464.7644705;
        double r62880 = r62878 + r62879;
        double r62881 = r62880 * r62874;
        double r62882 = 230661.510616;
        double r62883 = r62881 + r62882;
        double r62884 = r62883 * r62874;
        double r62885 = t;
        double r62886 = r62884 + r62885;
        double r62887 = a;
        double r62888 = r62874 + r62887;
        double r62889 = r62888 * r62874;
        double r62890 = b;
        double r62891 = r62889 + r62890;
        double r62892 = r62891 * r62874;
        double r62893 = c;
        double r62894 = r62892 + r62893;
        double r62895 = r62894 * r62874;
        double r62896 = i;
        double r62897 = r62895 + r62896;
        double r62898 = r62886 / r62897;
        return r62898;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62899 = x;
        double r62900 = y;
        double r62901 = r62899 * r62900;
        double r62902 = z;
        double r62903 = r62901 + r62902;
        double r62904 = cbrt(r62903);
        double r62905 = r62904 * r62904;
        double r62906 = r62904 * r62900;
        double r62907 = r62905 * r62906;
        double r62908 = 27464.7644705;
        double r62909 = r62907 + r62908;
        double r62910 = r62909 * r62900;
        double r62911 = 230661.510616;
        double r62912 = r62910 + r62911;
        double r62913 = r62912 * r62900;
        double r62914 = t;
        double r62915 = r62913 + r62914;
        double r62916 = a;
        double r62917 = r62900 + r62916;
        double r62918 = r62917 * r62900;
        double r62919 = b;
        double r62920 = r62918 + r62919;
        double r62921 = r62920 * r62900;
        double r62922 = c;
        double r62923 = r62921 + r62922;
        double r62924 = r62923 * r62900;
        double r62925 = i;
        double r62926 = r62924 + r62925;
        double r62927 = r62915 / r62926;
        return r62927;
}

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

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

  3. Applied add-cube-cbrt29.3

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

  4. Applied associate-*l*29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019308 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))