Average Error: 28.7 → 28.8
Time: 32.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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 r47912 = x;
        double r47913 = y;
        double r47914 = r47912 * r47913;
        double r47915 = z;
        double r47916 = r47914 + r47915;
        double r47917 = r47916 * r47913;
        double r47918 = 27464.7644705;
        double r47919 = r47917 + r47918;
        double r47920 = r47919 * r47913;
        double r47921 = 230661.510616;
        double r47922 = r47920 + r47921;
        double r47923 = r47922 * r47913;
        double r47924 = t;
        double r47925 = r47923 + r47924;
        double r47926 = a;
        double r47927 = r47913 + r47926;
        double r47928 = r47927 * r47913;
        double r47929 = b;
        double r47930 = r47928 + r47929;
        double r47931 = r47930 * r47913;
        double r47932 = c;
        double r47933 = r47931 + r47932;
        double r47934 = r47933 * r47913;
        double r47935 = i;
        double r47936 = r47934 + r47935;
        double r47937 = r47925 / r47936;
        return r47937;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r47938 = x;
        double r47939 = y;
        double r47940 = r47938 * r47939;
        double r47941 = z;
        double r47942 = r47940 + r47941;
        double r47943 = r47942 * r47939;
        double r47944 = 27464.7644705;
        double r47945 = r47943 + r47944;
        double r47946 = r47945 * r47939;
        double r47947 = 230661.510616;
        double r47948 = r47946 + r47947;
        double r47949 = r47948 * r47939;
        double r47950 = t;
        double r47951 = r47949 + r47950;
        double r47952 = 1.0;
        double r47953 = a;
        double r47954 = r47939 + r47953;
        double r47955 = r47954 * r47939;
        double r47956 = b;
        double r47957 = r47955 + r47956;
        double r47958 = r47957 * r47939;
        double r47959 = c;
        double r47960 = r47958 + r47959;
        double r47961 = r47960 * r47939;
        double r47962 = i;
        double r47963 = r47961 + r47962;
        double r47964 = r47952 / r47963;
        double r47965 = r47951 * r47964;
        return r47965;
}

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 28.7

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

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019323 
(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)))