Average Error: 29.0 → 29.1
Time: 36.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2486750 = x;
        double r2486751 = y;
        double r2486752 = r2486750 * r2486751;
        double r2486753 = z;
        double r2486754 = r2486752 + r2486753;
        double r2486755 = r2486754 * r2486751;
        double r2486756 = 27464.7644705;
        double r2486757 = r2486755 + r2486756;
        double r2486758 = r2486757 * r2486751;
        double r2486759 = 230661.510616;
        double r2486760 = r2486758 + r2486759;
        double r2486761 = r2486760 * r2486751;
        double r2486762 = t;
        double r2486763 = r2486761 + r2486762;
        double r2486764 = a;
        double r2486765 = r2486751 + r2486764;
        double r2486766 = r2486765 * r2486751;
        double r2486767 = b;
        double r2486768 = r2486766 + r2486767;
        double r2486769 = r2486768 * r2486751;
        double r2486770 = c;
        double r2486771 = r2486769 + r2486770;
        double r2486772 = r2486771 * r2486751;
        double r2486773 = i;
        double r2486774 = r2486772 + r2486773;
        double r2486775 = r2486763 / r2486774;
        return r2486775;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2486776 = y;
        double r2486777 = 230661.510616;
        double r2486778 = z;
        double r2486779 = x;
        double r2486780 = r2486779 * r2486776;
        double r2486781 = r2486778 + r2486780;
        double r2486782 = r2486776 * r2486781;
        double r2486783 = 27464.7644705;
        double r2486784 = r2486782 + r2486783;
        double r2486785 = r2486776 * r2486784;
        double r2486786 = cbrt(r2486785);
        double r2486787 = r2486786 * r2486786;
        double r2486788 = r2486786 * r2486787;
        double r2486789 = r2486777 + r2486788;
        double r2486790 = r2486776 * r2486789;
        double r2486791 = t;
        double r2486792 = r2486790 + r2486791;
        double r2486793 = c;
        double r2486794 = b;
        double r2486795 = a;
        double r2486796 = r2486776 + r2486795;
        double r2486797 = r2486776 * r2486796;
        double r2486798 = r2486794 + r2486797;
        double r2486799 = r2486798 * r2486776;
        double r2486800 = r2486793 + r2486799;
        double r2486801 = r2486776 * r2486800;
        double r2486802 = i;
        double r2486803 = r2486801 + r2486802;
        double r2486804 = r2486792 / r2486803;
        return r2486804;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.1

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification29.1

    \[\leadsto \frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]

Reproduce

herbie shell --seed 2019130 
(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)))