Average Error: 28.8 → 28.9
Time: 30.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3961817 = x;
        double r3961818 = y;
        double r3961819 = r3961817 * r3961818;
        double r3961820 = z;
        double r3961821 = r3961819 + r3961820;
        double r3961822 = r3961821 * r3961818;
        double r3961823 = 27464.7644705;
        double r3961824 = r3961822 + r3961823;
        double r3961825 = r3961824 * r3961818;
        double r3961826 = 230661.510616;
        double r3961827 = r3961825 + r3961826;
        double r3961828 = r3961827 * r3961818;
        double r3961829 = t;
        double r3961830 = r3961828 + r3961829;
        double r3961831 = a;
        double r3961832 = r3961818 + r3961831;
        double r3961833 = r3961832 * r3961818;
        double r3961834 = b;
        double r3961835 = r3961833 + r3961834;
        double r3961836 = r3961835 * r3961818;
        double r3961837 = c;
        double r3961838 = r3961836 + r3961837;
        double r3961839 = r3961838 * r3961818;
        double r3961840 = i;
        double r3961841 = r3961839 + r3961840;
        double r3961842 = r3961830 / r3961841;
        return r3961842;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3961843 = t;
        double r3961844 = y;
        double r3961845 = z;
        double r3961846 = x;
        double r3961847 = r3961846 * r3961844;
        double r3961848 = r3961845 + r3961847;
        double r3961849 = r3961844 * r3961848;
        double r3961850 = 27464.7644705;
        double r3961851 = r3961849 + r3961850;
        double r3961852 = r3961844 * r3961851;
        double r3961853 = 230661.510616;
        double r3961854 = r3961852 + r3961853;
        double r3961855 = r3961854 * r3961844;
        double r3961856 = r3961843 + r3961855;
        double r3961857 = c;
        double r3961858 = b;
        double r3961859 = a;
        double r3961860 = r3961844 + r3961859;
        double r3961861 = r3961860 * r3961844;
        double r3961862 = r3961858 + r3961861;
        double r3961863 = cbrt(r3961862);
        double r3961864 = r3961863 * r3961863;
        double r3961865 = r3961863 * r3961844;
        double r3961866 = r3961864 * r3961865;
        double r3961867 = r3961857 + r3961866;
        double r3961868 = r3961844 * r3961867;
        double r3961869 = i;
        double r3961870 = r3961868 + r3961869;
        double r3961871 = r3961856 / r3961870;
        return r3961871;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.9

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.9

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification28.9

    \[\leadsto \frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]

Reproduce

herbie shell --seed 2019172 
(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)))