Average Error: 28.6 → 28.6
Time: 32.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59717 = x;
        double r59718 = y;
        double r59719 = r59717 * r59718;
        double r59720 = z;
        double r59721 = r59719 + r59720;
        double r59722 = r59721 * r59718;
        double r59723 = 27464.7644705;
        double r59724 = r59722 + r59723;
        double r59725 = r59724 * r59718;
        double r59726 = 230661.510616;
        double r59727 = r59725 + r59726;
        double r59728 = r59727 * r59718;
        double r59729 = t;
        double r59730 = r59728 + r59729;
        double r59731 = a;
        double r59732 = r59718 + r59731;
        double r59733 = r59732 * r59718;
        double r59734 = b;
        double r59735 = r59733 + r59734;
        double r59736 = r59735 * r59718;
        double r59737 = c;
        double r59738 = r59736 + r59737;
        double r59739 = r59738 * r59718;
        double r59740 = i;
        double r59741 = r59739 + r59740;
        double r59742 = r59730 / r59741;
        return r59742;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59743 = x;
        double r59744 = y;
        double r59745 = r59743 * r59744;
        double r59746 = z;
        double r59747 = r59745 + r59746;
        double r59748 = r59747 * r59744;
        double r59749 = 27464.7644705;
        double r59750 = r59748 + r59749;
        double r59751 = r59750 * r59744;
        double r59752 = 230661.510616;
        double r59753 = r59751 + r59752;
        double r59754 = r59753 * r59744;
        double r59755 = t;
        double r59756 = r59754 + r59755;
        double r59757 = 1.0;
        double r59758 = a;
        double r59759 = r59744 + r59758;
        double r59760 = r59759 * r59744;
        double r59761 = b;
        double r59762 = r59760 + r59761;
        double r59763 = r59762 * r59744;
        double r59764 = c;
        double r59765 = r59763 + r59764;
        double r59766 = r59765 * r59744;
        double r59767 = i;
        double r59768 = r59766 + r59767;
        double r59769 = r59757 / r59768;
        double r59770 = r59756 * r59769;
        return r59770;
}

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 28.6

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

  3. Applied div-inv28.6

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.6

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))