Average Error: 28.8 → 28.9
Time: 2.4m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3850908 = x;
        double r3850909 = y;
        double r3850910 = r3850908 * r3850909;
        double r3850911 = z;
        double r3850912 = r3850910 + r3850911;
        double r3850913 = r3850912 * r3850909;
        double r3850914 = 27464.7644705;
        double r3850915 = r3850913 + r3850914;
        double r3850916 = r3850915 * r3850909;
        double r3850917 = 230661.510616;
        double r3850918 = r3850916 + r3850917;
        double r3850919 = r3850918 * r3850909;
        double r3850920 = t;
        double r3850921 = r3850919 + r3850920;
        double r3850922 = a;
        double r3850923 = r3850909 + r3850922;
        double r3850924 = r3850923 * r3850909;
        double r3850925 = b;
        double r3850926 = r3850924 + r3850925;
        double r3850927 = r3850926 * r3850909;
        double r3850928 = c;
        double r3850929 = r3850927 + r3850928;
        double r3850930 = r3850929 * r3850909;
        double r3850931 = i;
        double r3850932 = r3850930 + r3850931;
        double r3850933 = r3850921 / r3850932;
        return r3850933;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3850934 = t;
        double r3850935 = y;
        double r3850936 = z;
        double r3850937 = x;
        double r3850938 = r3850937 * r3850935;
        double r3850939 = r3850936 + r3850938;
        double r3850940 = r3850935 * r3850939;
        double r3850941 = 27464.7644705;
        double r3850942 = r3850940 + r3850941;
        double r3850943 = r3850935 * r3850942;
        double r3850944 = 230661.510616;
        double r3850945 = r3850943 + r3850944;
        double r3850946 = r3850945 * r3850935;
        double r3850947 = r3850934 + r3850946;
        double r3850948 = c;
        double r3850949 = b;
        double r3850950 = a;
        double r3850951 = r3850935 + r3850950;
        double r3850952 = r3850951 * r3850935;
        double r3850953 = r3850949 + r3850952;
        double r3850954 = cbrt(r3850953);
        double r3850955 = r3850954 * r3850954;
        double r3850956 = r3850954 * r3850935;
        double r3850957 = r3850955 * r3850956;
        double r3850958 = r3850948 + r3850957;
        double r3850959 = r3850935 * r3850958;
        double r3850960 = i;
        double r3850961 = r3850959 + r3850960;
        double r3850962 = r3850947 / r3850961;
        return r3850962;
}

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 28.8

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

  3. Applied add-cube-cbrt28.9

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

  4. Applied associate-*l*28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 
(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)))