Average Error: 28.8 → 28.8
Time: 22.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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 + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\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 r77789 = x;
        double r77790 = y;
        double r77791 = r77789 * r77790;
        double r77792 = z;
        double r77793 = r77791 + r77792;
        double r77794 = r77793 * r77790;
        double r77795 = 27464.7644705;
        double r77796 = r77794 + r77795;
        double r77797 = r77796 * r77790;
        double r77798 = 230661.510616;
        double r77799 = r77797 + r77798;
        double r77800 = r77799 * r77790;
        double r77801 = t;
        double r77802 = r77800 + r77801;
        double r77803 = a;
        double r77804 = r77790 + r77803;
        double r77805 = r77804 * r77790;
        double r77806 = b;
        double r77807 = r77805 + r77806;
        double r77808 = r77807 * r77790;
        double r77809 = c;
        double r77810 = r77808 + r77809;
        double r77811 = r77810 * r77790;
        double r77812 = i;
        double r77813 = r77811 + r77812;
        double r77814 = r77802 / r77813;
        return r77814;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77815 = x;
        double r77816 = y;
        double r77817 = r77815 * r77816;
        double r77818 = z;
        double r77819 = r77817 + r77818;
        double r77820 = r77819 * r77816;
        double r77821 = 471841060772561.0;
        double r77822 = 17179869184.0;
        double r77823 = r77821 / r77822;
        double r77824 = r77820 + r77823;
        double r77825 = r77824 * r77816;
        double r77826 = 7925469156333415.0;
        double r77827 = 34359738368.0;
        double r77828 = r77826 / r77827;
        double r77829 = r77825 + r77828;
        double r77830 = r77829 * r77816;
        double r77831 = t;
        double r77832 = r77830 + r77831;
        double r77833 = a;
        double r77834 = r77816 + r77833;
        double r77835 = r77834 * r77816;
        double r77836 = b;
        double r77837 = r77835 + r77836;
        double r77838 = r77837 * r77816;
        double r77839 = c;
        double r77840 = r77838 + r77839;
        double r77841 = r77840 * r77816;
        double r77842 = i;
        double r77843 = r77841 + r77842;
        double r77844 = r77832 / r77843;
        return r77844;
}

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 28.8

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

  3. Applied div-inv28.9

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

  4. Final simplification28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019303 
(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)))