Average Error: 28.7 → 28.8
Time: 12.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58815 = x;
        double r58816 = y;
        double r58817 = r58815 * r58816;
        double r58818 = z;
        double r58819 = r58817 + r58818;
        double r58820 = r58819 * r58816;
        double r58821 = 27464.7644705;
        double r58822 = r58820 + r58821;
        double r58823 = r58822 * r58816;
        double r58824 = 230661.510616;
        double r58825 = r58823 + r58824;
        double r58826 = r58825 * r58816;
        double r58827 = t;
        double r58828 = r58826 + r58827;
        double r58829 = a;
        double r58830 = r58816 + r58829;
        double r58831 = r58830 * r58816;
        double r58832 = b;
        double r58833 = r58831 + r58832;
        double r58834 = r58833 * r58816;
        double r58835 = c;
        double r58836 = r58834 + r58835;
        double r58837 = r58836 * r58816;
        double r58838 = i;
        double r58839 = r58837 + r58838;
        double r58840 = r58828 / r58839;
        return r58840;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58841 = x;
        double r58842 = y;
        double r58843 = r58841 * r58842;
        double r58844 = z;
        double r58845 = r58843 + r58844;
        double r58846 = r58845 * r58842;
        double r58847 = 27464.7644705;
        double r58848 = r58846 + r58847;
        double r58849 = r58848 * r58842;
        double r58850 = 230661.510616;
        double r58851 = r58849 + r58850;
        double r58852 = r58851 * r58842;
        double r58853 = t;
        double r58854 = r58852 + r58853;
        double r58855 = 1.0;
        double r58856 = a;
        double r58857 = r58842 + r58856;
        double r58858 = b;
        double r58859 = fma(r58857, r58842, r58858);
        double r58860 = c;
        double r58861 = fma(r58859, r58842, r58860);
        double r58862 = i;
        double r58863 = fma(r58861, r58842, r58862);
        double r58864 = r58863 * r58855;
        double r58865 = r58855 / r58864;
        double r58866 = r58854 * r58865;
        return r58866;
}

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 28.7

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]

Reproduce

herbie shell --seed 2020027 +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)))