Average Error: 29.6 → 29.7
Time: 8.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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}
↓
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71790 = x;
        double r71791 = y;
        double r71792 = r71790 * r71791;
        double r71793 = z;
        double r71794 = r71792 + r71793;
        double r71795 = r71794 * r71791;
        double r71796 = 27464.7644705;
        double r71797 = r71795 + r71796;
        double r71798 = r71797 * r71791;
        double r71799 = 230661.510616;
        double r71800 = r71798 + r71799;
        double r71801 = r71800 * r71791;
        double r71802 = t;
        double r71803 = r71801 + r71802;
        double r71804 = a;
        double r71805 = r71791 + r71804;
        double r71806 = r71805 * r71791;
        double r71807 = b;
        double r71808 = r71806 + r71807;
        double r71809 = r71808 * r71791;
        double r71810 = c;
        double r71811 = r71809 + r71810;
        double r71812 = r71811 * r71791;
        double r71813 = i;
        double r71814 = r71812 + r71813;
        double r71815 = r71803 / r71814;
        return r71815;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71816 = x;
        double r71817 = y;
        double r71818 = r71816 * r71817;
        double r71819 = z;
        double r71820 = r71818 + r71819;
        double r71821 = r71820 * r71817;
        double r71822 = 27464.7644705;
        double r71823 = r71821 + r71822;
        double r71824 = r71823 * r71817;
        double r71825 = 230661.510616;
        double r71826 = r71824 + r71825;
        double r71827 = r71826 * r71817;
        double r71828 = t;
        double r71829 = r71827 + r71828;
        double r71830 = a;
        double r71831 = r71817 + r71830;
        double r71832 = r71831 * r71817;
        double r71833 = b;
        double r71834 = r71832 + r71833;
        double r71835 = cbrt(r71834);
        double r71836 = r71835 * r71835;
        double r71837 = r71835 * r71817;
        double r71838 = r71836 * r71837;
        double r71839 = c;
        double r71840 = r71838 + r71839;
        double r71841 = r71840 * r71817;
        double r71842 = i;
        double r71843 = r71841 + r71842;
        double r71844 = r71829 / r71843;
        return r71844;
}

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 29.6

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

  3. Applied add-cube-cbrt29.7

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

  4. Applied associate-*l*29.7

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

  5. Final simplification29.7

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

Reproduce

herbie shell --seed 2020057 +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)))