Average Error: 29.1 → 29.3
Time: 2.1m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}{t + y \cdot \left(y \cdot \left(27464.7644704999984242022037506103515625 + y \cdot \left(z + x \cdot y\right)\right) + 230661.5106160000141244381666183471679688\right)}}\]
\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{1}{\frac{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}{t + y \cdot \left(y \cdot \left(27464.7644704999984242022037506103515625 + y \cdot \left(z + x \cdot y\right)\right) + 230661.5106160000141244381666183471679688\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r743887 = x;
        double r743888 = y;
        double r743889 = r743887 * r743888;
        double r743890 = z;
        double r743891 = r743889 + r743890;
        double r743892 = r743891 * r743888;
        double r743893 = 27464.7644705;
        double r743894 = r743892 + r743893;
        double r743895 = r743894 * r743888;
        double r743896 = 230661.510616;
        double r743897 = r743895 + r743896;
        double r743898 = r743897 * r743888;
        double r743899 = t;
        double r743900 = r743898 + r743899;
        double r743901 = a;
        double r743902 = r743888 + r743901;
        double r743903 = r743902 * r743888;
        double r743904 = b;
        double r743905 = r743903 + r743904;
        double r743906 = r743905 * r743888;
        double r743907 = c;
        double r743908 = r743906 + r743907;
        double r743909 = r743908 * r743888;
        double r743910 = i;
        double r743911 = r743909 + r743910;
        double r743912 = r743900 / r743911;
        return r743912;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r743913 = 1.0;
        double r743914 = y;
        double r743915 = c;
        double r743916 = b;
        double r743917 = a;
        double r743918 = r743914 + r743917;
        double r743919 = r743914 * r743918;
        double r743920 = r743916 + r743919;
        double r743921 = r743914 * r743920;
        double r743922 = r743915 + r743921;
        double r743923 = r743914 * r743922;
        double r743924 = i;
        double r743925 = r743923 + r743924;
        double r743926 = t;
        double r743927 = 27464.7644705;
        double r743928 = z;
        double r743929 = x;
        double r743930 = r743929 * r743914;
        double r743931 = r743928 + r743930;
        double r743932 = r743914 * r743931;
        double r743933 = r743927 + r743932;
        double r743934 = r743914 * r743933;
        double r743935 = 230661.510616;
        double r743936 = r743934 + r743935;
        double r743937 = r743914 * r743936;
        double r743938 = r743926 + r743937;
        double r743939 = r743925 / r743938;
        double r743940 = r743913 / r743939;
        return r743940;
}

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 29.1

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

  3. Applied add-cube-cbrt29.1

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

  4. Simplified29.1

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

  5. Simplified29.1

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

  7. Applied clear-num29.3

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

  8. Simplified29.3

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

  9. Final simplification29.3

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

Reproduce

herbie shell --seed 2019179 
(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)))