Average Error: 29.2 → 29.2
Time: 25.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{-\left(t + 230661.5106160000141244381666183471679688 \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)} - \frac{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(y \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}\]
\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{-\left(t + 230661.5106160000141244381666183471679688 \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)} - \frac{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(y \cdot y\right)}{-\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66888 = x;
        double r66889 = y;
        double r66890 = r66888 * r66889;
        double r66891 = z;
        double r66892 = r66890 + r66891;
        double r66893 = r66892 * r66889;
        double r66894 = 27464.7644705;
        double r66895 = r66893 + r66894;
        double r66896 = r66895 * r66889;
        double r66897 = 230661.510616;
        double r66898 = r66896 + r66897;
        double r66899 = r66898 * r66889;
        double r66900 = t;
        double r66901 = r66899 + r66900;
        double r66902 = a;
        double r66903 = r66889 + r66902;
        double r66904 = r66903 * r66889;
        double r66905 = b;
        double r66906 = r66904 + r66905;
        double r66907 = r66906 * r66889;
        double r66908 = c;
        double r66909 = r66907 + r66908;
        double r66910 = r66909 * r66889;
        double r66911 = i;
        double r66912 = r66910 + r66911;
        double r66913 = r66901 / r66912;
        return r66913;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66914 = t;
        double r66915 = 230661.510616;
        double r66916 = y;
        double r66917 = r66915 * r66916;
        double r66918 = r66914 + r66917;
        double r66919 = -r66918;
        double r66920 = a;
        double r66921 = r66916 + r66920;
        double r66922 = r66921 * r66916;
        double r66923 = b;
        double r66924 = r66922 + r66923;
        double r66925 = r66924 * r66916;
        double r66926 = c;
        double r66927 = r66925 + r66926;
        double r66928 = r66927 * r66916;
        double r66929 = i;
        double r66930 = r66928 + r66929;
        double r66931 = -r66930;
        double r66932 = r66919 / r66931;
        double r66933 = x;
        double r66934 = r66933 * r66916;
        double r66935 = z;
        double r66936 = r66934 + r66935;
        double r66937 = r66936 * r66916;
        double r66938 = 27464.7644705;
        double r66939 = r66937 + r66938;
        double r66940 = r66916 * r66916;
        double r66941 = r66939 * r66940;
        double r66942 = r66941 / r66931;
        double r66943 = r66932 - r66942;
        return r66943;
}

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 29.2

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

  3. Applied add-cube-cbrt29.3

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

  4. Applied associate-*r*29.3

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

  6. Applied frac-2neg29.3

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

  7. Simplified29.2

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

  9. Applied distribute-lft-neg-out29.2

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

  10. Applied unsub-neg29.2

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

  11. Applied div-sub29.2

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

  12. Final simplification29.2

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

Reproduce

herbie shell --seed 2019297 
(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)))