Average Error: 29.6 → 29.7
Time: 8.5s
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 r63804 = x;
        double r63805 = y;
        double r63806 = r63804 * r63805;
        double r63807 = z;
        double r63808 = r63806 + r63807;
        double r63809 = r63808 * r63805;
        double r63810 = 27464.7644705;
        double r63811 = r63809 + r63810;
        double r63812 = r63811 * r63805;
        double r63813 = 230661.510616;
        double r63814 = r63812 + r63813;
        double r63815 = r63814 * r63805;
        double r63816 = t;
        double r63817 = r63815 + r63816;
        double r63818 = a;
        double r63819 = r63805 + r63818;
        double r63820 = r63819 * r63805;
        double r63821 = b;
        double r63822 = r63820 + r63821;
        double r63823 = r63822 * r63805;
        double r63824 = c;
        double r63825 = r63823 + r63824;
        double r63826 = r63825 * r63805;
        double r63827 = i;
        double r63828 = r63826 + r63827;
        double r63829 = r63817 / r63828;
        return r63829;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63830 = x;
        double r63831 = y;
        double r63832 = r63830 * r63831;
        double r63833 = z;
        double r63834 = r63832 + r63833;
        double r63835 = r63834 * r63831;
        double r63836 = 27464.7644705;
        double r63837 = r63835 + r63836;
        double r63838 = r63837 * r63831;
        double r63839 = 230661.510616;
        double r63840 = r63838 + r63839;
        double r63841 = r63840 * r63831;
        double r63842 = t;
        double r63843 = r63841 + r63842;
        double r63844 = a;
        double r63845 = r63831 + r63844;
        double r63846 = r63845 * r63831;
        double r63847 = b;
        double r63848 = r63846 + r63847;
        double r63849 = cbrt(r63848);
        double r63850 = r63849 * r63849;
        double r63851 = r63849 * r63831;
        double r63852 = r63850 * r63851;
        double r63853 = c;
        double r63854 = r63852 + r63853;
        double r63855 = r63854 * r63831;
        double r63856 = i;
        double r63857 = r63855 + r63856;
        double r63858 = r63843 / r63857;
        return r63858;
}

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)))