Average Error: 29.2 → 28.5
Time: 9.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.9235959509009306 \cdot 10^{289}:\\ \;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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}
↓
\begin{array}{l}
\mathbf{if}\;\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} \le 2.9235959509009306 \cdot 10^{289}:\\
\;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\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}\\

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61796 = x;
        double r61797 = y;
        double r61798 = r61796 * r61797;
        double r61799 = z;
        double r61800 = r61798 + r61799;
        double r61801 = r61800 * r61797;
        double r61802 = 27464.7644705;
        double r61803 = r61801 + r61802;
        double r61804 = r61803 * r61797;
        double r61805 = 230661.510616;
        double r61806 = r61804 + r61805;
        double r61807 = r61806 * r61797;
        double r61808 = t;
        double r61809 = r61807 + r61808;
        double r61810 = a;
        double r61811 = r61797 + r61810;
        double r61812 = r61811 * r61797;
        double r61813 = b;
        double r61814 = r61812 + r61813;
        double r61815 = r61814 * r61797;
        double r61816 = c;
        double r61817 = r61815 + r61816;
        double r61818 = r61817 * r61797;
        double r61819 = i;
        double r61820 = r61818 + r61819;
        double r61821 = r61809 / r61820;
        return r61821;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61822 = x;
        double r61823 = y;
        double r61824 = r61822 * r61823;
        double r61825 = z;
        double r61826 = r61824 + r61825;
        double r61827 = r61826 * r61823;
        double r61828 = 27464.7644705;
        double r61829 = r61827 + r61828;
        double r61830 = r61829 * r61823;
        double r61831 = 230661.510616;
        double r61832 = r61830 + r61831;
        double r61833 = r61832 * r61823;
        double r61834 = t;
        double r61835 = r61833 + r61834;
        double r61836 = a;
        double r61837 = r61823 + r61836;
        double r61838 = r61837 * r61823;
        double r61839 = b;
        double r61840 = r61838 + r61839;
        double r61841 = r61840 * r61823;
        double r61842 = c;
        double r61843 = r61841 + r61842;
        double r61844 = r61843 * r61823;
        double r61845 = i;
        double r61846 = r61844 + r61845;
        double r61847 = r61835 / r61846;
        double r61848 = 2.9235959509009306e+289;
        bool r61849 = r61847 <= r61848;
        double r61850 = cbrt(r61827);
        double r61851 = r61850 * r61850;
        double r61852 = r61851 * r61850;
        double r61853 = r61852 + r61828;
        double r61854 = r61853 * r61823;
        double r61855 = r61854 + r61831;
        double r61856 = r61855 * r61823;
        double r61857 = r61856 + r61834;
        double r61858 = r61857 / r61846;
        double r61859 = 0.0;
        double r61860 = r61849 ? r61858 : r61859;
        return r61860;
}

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. Split input into 2 regimes

  2. if (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) < 2.9235959509009306e+289

    1. Initial program 5.6

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

    3. Applied add-cube-cbrt5.7

      \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

    if 2.9235959509009306e+289 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

    1. Initial program 63.7

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

    2. Taylor expanded around 0 61.7

      \[\leadsto \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification28.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.9235959509009306 \cdot 10^{289}:\\ \;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 +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)))