Average Error: 29.2 → 29.8
Time: 35.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y} \cdot \sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}\]
\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{\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y} \cdot \sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5636873 = x;
        double r5636874 = y;
        double r5636875 = r5636873 * r5636874;
        double r5636876 = z;
        double r5636877 = r5636875 + r5636876;
        double r5636878 = r5636877 * r5636874;
        double r5636879 = 27464.7644705;
        double r5636880 = r5636878 + r5636879;
        double r5636881 = r5636880 * r5636874;
        double r5636882 = 230661.510616;
        double r5636883 = r5636881 + r5636882;
        double r5636884 = r5636883 * r5636874;
        double r5636885 = t;
        double r5636886 = r5636884 + r5636885;
        double r5636887 = a;
        double r5636888 = r5636874 + r5636887;
        double r5636889 = r5636888 * r5636874;
        double r5636890 = b;
        double r5636891 = r5636889 + r5636890;
        double r5636892 = r5636891 * r5636874;
        double r5636893 = c;
        double r5636894 = r5636892 + r5636893;
        double r5636895 = r5636894 * r5636874;
        double r5636896 = i;
        double r5636897 = r5636895 + r5636896;
        double r5636898 = r5636886 / r5636897;
        return r5636898;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5636899 = t;
        double r5636900 = y;
        double r5636901 = z;
        double r5636902 = x;
        double r5636903 = r5636902 * r5636900;
        double r5636904 = r5636901 + r5636903;
        double r5636905 = r5636900 * r5636904;
        double r5636906 = 27464.7644705;
        double r5636907 = r5636905 + r5636906;
        double r5636908 = r5636900 * r5636907;
        double r5636909 = 230661.510616;
        double r5636910 = r5636908 + r5636909;
        double r5636911 = r5636910 * r5636900;
        double r5636912 = r5636899 + r5636911;
        double r5636913 = i;
        double r5636914 = c;
        double r5636915 = b;
        double r5636916 = a;
        double r5636917 = r5636900 + r5636916;
        double r5636918 = r5636917 * r5636900;
        double r5636919 = r5636915 + r5636918;
        double r5636920 = r5636900 * r5636919;
        double r5636921 = r5636914 + r5636920;
        double r5636922 = r5636921 * r5636900;
        double r5636923 = r5636913 + r5636922;
        double r5636924 = cbrt(r5636923);
        double r5636925 = r5636924 * r5636924;
        double r5636926 = r5636912 / r5636925;
        double r5636927 = r5636926 / r5636924;
        return r5636927;
}

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-cbrt29.8

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

  4. Applied associate-/r*29.8

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

  5. Final simplification29.8

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))