Average Error: 28.8 → 28.9
Time: 2.3m
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 r3987776 = x;
        double r3987777 = y;
        double r3987778 = r3987776 * r3987777;
        double r3987779 = z;
        double r3987780 = r3987778 + r3987779;
        double r3987781 = r3987780 * r3987777;
        double r3987782 = 27464.7644705;
        double r3987783 = r3987781 + r3987782;
        double r3987784 = r3987783 * r3987777;
        double r3987785 = 230661.510616;
        double r3987786 = r3987784 + r3987785;
        double r3987787 = r3987786 * r3987777;
        double r3987788 = t;
        double r3987789 = r3987787 + r3987788;
        double r3987790 = a;
        double r3987791 = r3987777 + r3987790;
        double r3987792 = r3987791 * r3987777;
        double r3987793 = b;
        double r3987794 = r3987792 + r3987793;
        double r3987795 = r3987794 * r3987777;
        double r3987796 = c;
        double r3987797 = r3987795 + r3987796;
        double r3987798 = r3987797 * r3987777;
        double r3987799 = i;
        double r3987800 = r3987798 + r3987799;
        double r3987801 = r3987789 / r3987800;
        return r3987801;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3987802 = t;
        double r3987803 = y;
        double r3987804 = z;
        double r3987805 = x;
        double r3987806 = r3987805 * r3987803;
        double r3987807 = r3987804 + r3987806;
        double r3987808 = r3987803 * r3987807;
        double r3987809 = 27464.7644705;
        double r3987810 = r3987808 + r3987809;
        double r3987811 = r3987803 * r3987810;
        double r3987812 = 230661.510616;
        double r3987813 = r3987811 + r3987812;
        double r3987814 = r3987813 * r3987803;
        double r3987815 = r3987802 + r3987814;
        double r3987816 = c;
        double r3987817 = b;
        double r3987818 = a;
        double r3987819 = r3987803 + r3987818;
        double r3987820 = r3987819 * r3987803;
        double r3987821 = r3987817 + r3987820;
        double r3987822 = cbrt(r3987821);
        double r3987823 = r3987822 * r3987822;
        double r3987824 = r3987822 * r3987803;
        double r3987825 = r3987823 * r3987824;
        double r3987826 = r3987816 + r3987825;
        double r3987827 = r3987803 * r3987826;
        double r3987828 = i;
        double r3987829 = r3987827 + r3987828;
        double r3987830 = r3987815 / r3987829;
        return r3987830;
}

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)))