Average Error: 28.7 → 28.8
Time: 15.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\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}
↓
\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(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\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 r62802 = x;
        double r62803 = y;
        double r62804 = r62802 * r62803;
        double r62805 = z;
        double r62806 = r62804 + r62805;
        double r62807 = r62806 * r62803;
        double r62808 = 27464.7644705;
        double r62809 = r62807 + r62808;
        double r62810 = r62809 * r62803;
        double r62811 = 230661.510616;
        double r62812 = r62810 + r62811;
        double r62813 = r62812 * r62803;
        double r62814 = t;
        double r62815 = r62813 + r62814;
        double r62816 = a;
        double r62817 = r62803 + r62816;
        double r62818 = r62817 * r62803;
        double r62819 = b;
        double r62820 = r62818 + r62819;
        double r62821 = r62820 * r62803;
        double r62822 = c;
        double r62823 = r62821 + r62822;
        double r62824 = r62823 * r62803;
        double r62825 = i;
        double r62826 = r62824 + r62825;
        double r62827 = r62815 / r62826;
        return r62827;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62828 = x;
        double r62829 = y;
        double r62830 = r62828 * r62829;
        double r62831 = z;
        double r62832 = r62830 + r62831;
        double r62833 = r62832 * r62829;
        double r62834 = 27464.7644705;
        double r62835 = r62833 + r62834;
        double r62836 = r62835 * r62829;
        double r62837 = 230661.510616;
        double r62838 = r62836 + r62837;
        double r62839 = r62838 * r62829;
        double r62840 = t;
        double r62841 = r62839 + r62840;
        double r62842 = 1.0;
        double r62843 = b;
        double r62844 = r62829 * r62843;
        double r62845 = 3.0;
        double r62846 = pow(r62829, r62845);
        double r62847 = a;
        double r62848 = 2.0;
        double r62849 = pow(r62829, r62848);
        double r62850 = r62847 * r62849;
        double r62851 = r62846 + r62850;
        double r62852 = r62844 + r62851;
        double r62853 = c;
        double r62854 = r62852 + r62853;
        double r62855 = r62854 * r62829;
        double r62856 = i;
        double r62857 = r62855 + r62856;
        double r62858 = r62842 / r62857;
        double r62859 = r62841 * r62858;
        return r62859;
}

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 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. Taylor expanded around inf 28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020047 
(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)))