Average Error: 29.2 → 29.3
Time: 2.4m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{i + y \cdot \left(\left(\left(y \cdot y\right) \cdot \left(y + a\right) + y \cdot b\right) + c\right)}\]
\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}{i + y \cdot \left(\left(\left(y \cdot y\right) \cdot \left(y + a\right) + y \cdot b\right) + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r744718 = x;
        double r744719 = y;
        double r744720 = r744718 * r744719;
        double r744721 = z;
        double r744722 = r744720 + r744721;
        double r744723 = r744722 * r744719;
        double r744724 = 27464.7644705;
        double r744725 = r744723 + r744724;
        double r744726 = r744725 * r744719;
        double r744727 = 230661.510616;
        double r744728 = r744726 + r744727;
        double r744729 = r744728 * r744719;
        double r744730 = t;
        double r744731 = r744729 + r744730;
        double r744732 = a;
        double r744733 = r744719 + r744732;
        double r744734 = r744733 * r744719;
        double r744735 = b;
        double r744736 = r744734 + r744735;
        double r744737 = r744736 * r744719;
        double r744738 = c;
        double r744739 = r744737 + r744738;
        double r744740 = r744739 * r744719;
        double r744741 = i;
        double r744742 = r744740 + r744741;
        double r744743 = r744731 / r744742;
        return r744743;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r744744 = t;
        double r744745 = y;
        double r744746 = z;
        double r744747 = x;
        double r744748 = r744747 * r744745;
        double r744749 = r744746 + r744748;
        double r744750 = r744745 * r744749;
        double r744751 = 27464.7644705;
        double r744752 = r744750 + r744751;
        double r744753 = r744745 * r744752;
        double r744754 = 230661.510616;
        double r744755 = r744753 + r744754;
        double r744756 = r744755 * r744745;
        double r744757 = r744744 + r744756;
        double r744758 = i;
        double r744759 = r744745 * r744745;
        double r744760 = a;
        double r744761 = r744745 + r744760;
        double r744762 = r744759 * r744761;
        double r744763 = b;
        double r744764 = r744745 * r744763;
        double r744765 = r744762 + r744764;
        double r744766 = c;
        double r744767 = r744765 + r744766;
        double r744768 = r744745 * r744767;
        double r744769 = r744758 + r744768;
        double r744770 = r744757 / r744769;
        return r744770;
}

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 29.2

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

  2. Taylor expanded around inf 29.3

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(a \cdot {y}^{2} + \left({y}^{3} + y \cdot b\right)\right)} + c\right) \cdot y + i}\]

  3. Simplified29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2019174 
(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)))