Average Error: 29.2 → 29.2
Time: 32.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73784 = x;
        double r73785 = y;
        double r73786 = r73784 * r73785;
        double r73787 = z;
        double r73788 = r73786 + r73787;
        double r73789 = r73788 * r73785;
        double r73790 = 27464.7644705;
        double r73791 = r73789 + r73790;
        double r73792 = r73791 * r73785;
        double r73793 = 230661.510616;
        double r73794 = r73792 + r73793;
        double r73795 = r73794 * r73785;
        double r73796 = t;
        double r73797 = r73795 + r73796;
        double r73798 = a;
        double r73799 = r73785 + r73798;
        double r73800 = r73799 * r73785;
        double r73801 = b;
        double r73802 = r73800 + r73801;
        double r73803 = r73802 * r73785;
        double r73804 = c;
        double r73805 = r73803 + r73804;
        double r73806 = r73805 * r73785;
        double r73807 = i;
        double r73808 = r73806 + r73807;
        double r73809 = r73797 / r73808;
        return r73809;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73810 = x;
        double r73811 = y;
        double r73812 = z;
        double r73813 = fma(r73810, r73811, r73812);
        double r73814 = 27464.7644705;
        double r73815 = fma(r73813, r73811, r73814);
        double r73816 = 230661.510616;
        double r73817 = fma(r73815, r73811, r73816);
        double r73818 = t;
        double r73819 = fma(r73817, r73811, r73818);
        double r73820 = a;
        double r73821 = r73811 + r73820;
        double r73822 = b;
        double r73823 = fma(r73821, r73811, r73822);
        double r73824 = c;
        double r73825 = fma(r73823, r73811, r73824);
        double r73826 = i;
        double r73827 = fma(r73825, r73811, r73826);
        double r73828 = r73819 / r73827;
        return r73828;
}

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

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. Simplified29.2

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

  3. Final simplification29.2

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))