Average Error: 29.0 → 29.3
Time: 2.1m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\left(i + \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y\right) \cdot \frac{1}{t + y \cdot \left(230661.510616000014 + \left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y\right)}}\]
\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{1}{\left(i + \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y\right) \cdot \frac{1}{t + y \cdot \left(230661.510616000014 + \left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r763806 = x;
        double r763807 = y;
        double r763808 = r763806 * r763807;
        double r763809 = z;
        double r763810 = r763808 + r763809;
        double r763811 = r763810 * r763807;
        double r763812 = 27464.7644705;
        double r763813 = r763811 + r763812;
        double r763814 = r763813 * r763807;
        double r763815 = 230661.510616;
        double r763816 = r763814 + r763815;
        double r763817 = r763816 * r763807;
        double r763818 = t;
        double r763819 = r763817 + r763818;
        double r763820 = a;
        double r763821 = r763807 + r763820;
        double r763822 = r763821 * r763807;
        double r763823 = b;
        double r763824 = r763822 + r763823;
        double r763825 = r763824 * r763807;
        double r763826 = c;
        double r763827 = r763825 + r763826;
        double r763828 = r763827 * r763807;
        double r763829 = i;
        double r763830 = r763828 + r763829;
        double r763831 = r763819 / r763830;
        return r763831;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r763832 = 1.0;
        double r763833 = i;
        double r763834 = y;
        double r763835 = a;
        double r763836 = r763834 + r763835;
        double r763837 = r763836 * r763834;
        double r763838 = b;
        double r763839 = r763837 + r763838;
        double r763840 = r763839 * r763834;
        double r763841 = c;
        double r763842 = r763840 + r763841;
        double r763843 = r763842 * r763834;
        double r763844 = r763833 + r763843;
        double r763845 = t;
        double r763846 = 230661.510616;
        double r763847 = x;
        double r763848 = r763847 * r763834;
        double r763849 = z;
        double r763850 = r763848 + r763849;
        double r763851 = r763850 * r763834;
        double r763852 = 27464.7644705;
        double r763853 = r763851 + r763852;
        double r763854 = r763853 * r763834;
        double r763855 = r763846 + r763854;
        double r763856 = r763834 * r763855;
        double r763857 = r763845 + r763856;
        double r763858 = r763832 / r763857;
        double r763859 = r763844 * r763858;
        double r763860 = r763832 / r763859;
        return r763860;
}

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 29.0

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

  3. Applied add-cube-cbrt29.1

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

  4. Applied associate-*l*29.1

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

  6. Applied clear-num29.4

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot y\right) + 230661.510616000014\right) \cdot y + t}}}\]

  7. Simplified29.3

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

  9. Applied div-inv29.3

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

  10. Final simplification29.3

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))