Average Error: 29.6 → 29.6
Time: 7.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\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 r57883 = x;
        double r57884 = y;
        double r57885 = r57883 * r57884;
        double r57886 = z;
        double r57887 = r57885 + r57886;
        double r57888 = r57887 * r57884;
        double r57889 = 27464.7644705;
        double r57890 = r57888 + r57889;
        double r57891 = r57890 * r57884;
        double r57892 = 230661.510616;
        double r57893 = r57891 + r57892;
        double r57894 = r57893 * r57884;
        double r57895 = t;
        double r57896 = r57894 + r57895;
        double r57897 = a;
        double r57898 = r57884 + r57897;
        double r57899 = r57898 * r57884;
        double r57900 = b;
        double r57901 = r57899 + r57900;
        double r57902 = r57901 * r57884;
        double r57903 = c;
        double r57904 = r57902 + r57903;
        double r57905 = r57904 * r57884;
        double r57906 = i;
        double r57907 = r57905 + r57906;
        double r57908 = r57896 / r57907;
        return r57908;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57909 = x;
        double r57910 = y;
        double r57911 = r57909 * r57910;
        double r57912 = z;
        double r57913 = r57911 + r57912;
        double r57914 = r57913 * r57910;
        double r57915 = 27464.7644705;
        double r57916 = r57914 + r57915;
        double r57917 = r57916 * r57910;
        double r57918 = 230661.510616;
        double r57919 = r57917 + r57918;
        double r57920 = r57919 * r57910;
        double r57921 = t;
        double r57922 = r57920 + r57921;
        double r57923 = a;
        double r57924 = r57910 + r57923;
        double r57925 = r57924 * r57910;
        double r57926 = b;
        double r57927 = r57925 + r57926;
        double r57928 = r57927 * r57910;
        double r57929 = c;
        double r57930 = r57928 + r57929;
        double r57931 = r57930 * r57910;
        double r57932 = i;
        double r57933 = r57931 + r57932;
        double r57934 = r57922 / r57933;
        return r57934;
}

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 29.6

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied clear-num29.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity29.8

    \[\leadsto \frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}}}\]

  6. Applied *-un-lft-identity29.8

    \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}}\]

  7. Applied times-frac29.8

    \[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  8. Applied add-cube-cbrt29.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

  9. Applied times-frac29.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  10. Simplified29.8

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

  11. Simplified29.6

    \[\leadsto 1 \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  12. Final simplification29.6

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020057 
(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)))