Average Error: 28.8 → 28.9
Time: 7.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60809 = x;
        double r60810 = y;
        double r60811 = r60809 * r60810;
        double r60812 = z;
        double r60813 = r60811 + r60812;
        double r60814 = r60813 * r60810;
        double r60815 = 27464.7644705;
        double r60816 = r60814 + r60815;
        double r60817 = r60816 * r60810;
        double r60818 = 230661.510616;
        double r60819 = r60817 + r60818;
        double r60820 = r60819 * r60810;
        double r60821 = t;
        double r60822 = r60820 + r60821;
        double r60823 = a;
        double r60824 = r60810 + r60823;
        double r60825 = r60824 * r60810;
        double r60826 = b;
        double r60827 = r60825 + r60826;
        double r60828 = r60827 * r60810;
        double r60829 = c;
        double r60830 = r60828 + r60829;
        double r60831 = r60830 * r60810;
        double r60832 = i;
        double r60833 = r60831 + r60832;
        double r60834 = r60822 / r60833;
        return r60834;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60835 = x;
        double r60836 = y;
        double r60837 = r60835 * r60836;
        double r60838 = z;
        double r60839 = r60837 + r60838;
        double r60840 = cbrt(r60839);
        double r60841 = r60840 * r60840;
        double r60842 = r60840 * r60836;
        double r60843 = r60841 * r60842;
        double r60844 = 27464.7644705;
        double r60845 = r60843 + r60844;
        double r60846 = r60845 * r60836;
        double r60847 = 230661.510616;
        double r60848 = r60846 + r60847;
        double r60849 = r60848 * r60836;
        double r60850 = t;
        double r60851 = r60849 + r60850;
        double r60852 = 1.0;
        double r60853 = a;
        double r60854 = r60836 + r60853;
        double r60855 = r60854 * r60836;
        double r60856 = b;
        double r60857 = r60855 + r60856;
        double r60858 = r60857 * r60836;
        double r60859 = c;
        double r60860 = r60858 + r60859;
        double r60861 = r60860 * r60836;
        double r60862 = i;
        double r60863 = r60861 + r60862;
        double r60864 = r60852 / r60863;
        double r60865 = r60851 * r60864;
        return r60865;
}

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 28.8

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

  3. Applied div-inv28.8

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

  5. Applied add-cube-cbrt28.9

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

  6. Applied associate-*l*28.9

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

  7. Final simplification28.9

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

Reproduce

herbie shell --seed 2020056 
(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)))