Average Error: 28.9 → 28.9
Time: 12.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(t + y \cdot 230661.5106160000141244381666183471679688\right) + y \cdot {\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right)}^{3}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(t + y \cdot 230661.5106160000141244381666183471679688\right) + y \cdot {\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right)}^{3}}{\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 r99882 = x;
        double r99883 = y;
        double r99884 = r99882 * r99883;
        double r99885 = z;
        double r99886 = r99884 + r99885;
        double r99887 = r99886 * r99883;
        double r99888 = 27464.7644705;
        double r99889 = r99887 + r99888;
        double r99890 = r99889 * r99883;
        double r99891 = 230661.510616;
        double r99892 = r99890 + r99891;
        double r99893 = r99892 * r99883;
        double r99894 = t;
        double r99895 = r99893 + r99894;
        double r99896 = a;
        double r99897 = r99883 + r99896;
        double r99898 = r99897 * r99883;
        double r99899 = b;
        double r99900 = r99898 + r99899;
        double r99901 = r99900 * r99883;
        double r99902 = c;
        double r99903 = r99901 + r99902;
        double r99904 = r99903 * r99883;
        double r99905 = i;
        double r99906 = r99904 + r99905;
        double r99907 = r99895 / r99906;
        return r99907;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r99908 = t;
        double r99909 = y;
        double r99910 = 230661.510616;
        double r99911 = r99909 * r99910;
        double r99912 = r99908 + r99911;
        double r99913 = x;
        double r99914 = r99913 * r99909;
        double r99915 = z;
        double r99916 = r99914 + r99915;
        double r99917 = r99916 * r99909;
        double r99918 = 27464.7644705;
        double r99919 = r99917 + r99918;
        double r99920 = r99919 * r99909;
        double r99921 = cbrt(r99920);
        double r99922 = 3.0;
        double r99923 = pow(r99921, r99922);
        double r99924 = r99909 * r99923;
        double r99925 = r99912 + r99924;
        double r99926 = a;
        double r99927 = r99909 + r99926;
        double r99928 = r99927 * r99909;
        double r99929 = b;
        double r99930 = r99928 + r99929;
        double r99931 = r99930 * r99909;
        double r99932 = c;
        double r99933 = r99931 + r99932;
        double r99934 = r99933 * r99909;
        double r99935 = i;
        double r99936 = r99934 + r99935;
        double r99937 = r99925 / r99936;
        return r99937;
}

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 28.9

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

  3. Applied add-cube-cbrt28.9

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

  5. Applied *-un-lft-identity28.9

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\color{blue}{1 \cdot \left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}}\]

  6. Applied associate-/r*28.9

    \[\leadsto \color{blue}{\frac{\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{1}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  7. Simplified28.9

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

  8. Final simplification28.9

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

Reproduce

herbie shell --seed 2019322 
(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)))