Average Error: 29.2 → 29.2
Time: 15.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\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(\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60828 = x;
        double r60829 = y;
        double r60830 = r60828 * r60829;
        double r60831 = z;
        double r60832 = r60830 + r60831;
        double r60833 = r60832 * r60829;
        double r60834 = 27464.7644705;
        double r60835 = r60833 + r60834;
        double r60836 = r60835 * r60829;
        double r60837 = 230661.510616;
        double r60838 = r60836 + r60837;
        double r60839 = r60838 * r60829;
        double r60840 = t;
        double r60841 = r60839 + r60840;
        double r60842 = a;
        double r60843 = r60829 + r60842;
        double r60844 = r60843 * r60829;
        double r60845 = b;
        double r60846 = r60844 + r60845;
        double r60847 = r60846 * r60829;
        double r60848 = c;
        double r60849 = r60847 + r60848;
        double r60850 = r60849 * r60829;
        double r60851 = i;
        double r60852 = r60850 + r60851;
        double r60853 = r60841 / r60852;
        return r60853;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60854 = x;
        double r60855 = y;
        double r60856 = r60854 * r60855;
        double r60857 = z;
        double r60858 = r60856 + r60857;
        double r60859 = r60858 * r60855;
        double r60860 = 27464.7644705;
        double r60861 = r60859 + r60860;
        double r60862 = r60861 * r60855;
        double r60863 = 230661.510616;
        double r60864 = r60862 + r60863;
        double r60865 = r60864 * r60855;
        double r60866 = t;
        double r60867 = r60865 + r60866;
        double r60868 = a;
        double r60869 = r60855 + r60868;
        double r60870 = r60869 * r60855;
        double r60871 = b;
        double r60872 = r60870 + r60871;
        double r60873 = r60872 * r60855;
        double r60874 = c;
        double r60875 = r60873 + r60874;
        double r60876 = r60875 * r60855;
        double r60877 = i;
        double r60878 = r60876 + r60877;
        double r60879 = r60867 / r60878;
        return r60879;
}

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 div-inv29.3

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 1978988140 
(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)))