Average Error: 29.0 → 29.0
Time: 40.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left(y \cdot y\right) \cdot \left(a + y\right)\right) + c\right) \cdot y + i}\]
\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}
↓
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left(y \cdot y\right) \cdot \left(a + y\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 r67702 = x;
        double r67703 = y;
        double r67704 = r67702 * r67703;
        double r67705 = z;
        double r67706 = r67704 + r67705;
        double r67707 = r67706 * r67703;
        double r67708 = 27464.7644705;
        double r67709 = r67707 + r67708;
        double r67710 = r67709 * r67703;
        double r67711 = 230661.510616;
        double r67712 = r67710 + r67711;
        double r67713 = r67712 * r67703;
        double r67714 = t;
        double r67715 = r67713 + r67714;
        double r67716 = a;
        double r67717 = r67703 + r67716;
        double r67718 = r67717 * r67703;
        double r67719 = b;
        double r67720 = r67718 + r67719;
        double r67721 = r67720 * r67703;
        double r67722 = c;
        double r67723 = r67721 + r67722;
        double r67724 = r67723 * r67703;
        double r67725 = i;
        double r67726 = r67724 + r67725;
        double r67727 = r67715 / r67726;
        return r67727;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67728 = x;
        double r67729 = y;
        double r67730 = r67728 * r67729;
        double r67731 = z;
        double r67732 = r67730 + r67731;
        double r67733 = r67732 * r67729;
        double r67734 = 27464.7644705;
        double r67735 = r67733 + r67734;
        double r67736 = r67735 * r67729;
        double r67737 = 230661.510616;
        double r67738 = r67736 + r67737;
        double r67739 = r67738 * r67729;
        double r67740 = t;
        double r67741 = r67739 + r67740;
        double r67742 = b;
        double r67743 = r67729 * r67742;
        double r67744 = r67729 * r67729;
        double r67745 = a;
        double r67746 = r67745 + r67729;
        double r67747 = r67744 * r67746;
        double r67748 = r67743 + r67747;
        double r67749 = c;
        double r67750 = r67748 + r67749;
        double r67751 = r67750 * r67729;
        double r67752 = i;
        double r67753 = r67751 + r67752;
        double r67754 = r67741 / r67753;
        return r67754;
}

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

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

  2. Taylor expanded around inf 29.0

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

  3. Simplified29.0

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

  4. Final simplification29.0

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

Reproduce

herbie shell --seed 2019199 
(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)))