Average Error: 29.2 → 29.3
Time: 9.5s
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 r61724 = x;
        double r61725 = y;
        double r61726 = r61724 * r61725;
        double r61727 = z;
        double r61728 = r61726 + r61727;
        double r61729 = r61728 * r61725;
        double r61730 = 27464.7644705;
        double r61731 = r61729 + r61730;
        double r61732 = r61731 * r61725;
        double r61733 = 230661.510616;
        double r61734 = r61732 + r61733;
        double r61735 = r61734 * r61725;
        double r61736 = t;
        double r61737 = r61735 + r61736;
        double r61738 = a;
        double r61739 = r61725 + r61738;
        double r61740 = r61739 * r61725;
        double r61741 = b;
        double r61742 = r61740 + r61741;
        double r61743 = r61742 * r61725;
        double r61744 = c;
        double r61745 = r61743 + r61744;
        double r61746 = r61745 * r61725;
        double r61747 = i;
        double r61748 = r61746 + r61747;
        double r61749 = r61737 / r61748;
        return r61749;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61750 = x;
        double r61751 = y;
        double r61752 = r61750 * r61751;
        double r61753 = z;
        double r61754 = r61752 + r61753;
        double r61755 = r61754 * r61751;
        double r61756 = 27464.7644705;
        double r61757 = r61755 + r61756;
        double r61758 = r61757 * r61751;
        double r61759 = 230661.510616;
        double r61760 = r61758 + r61759;
        double r61761 = r61760 * r61751;
        double r61762 = t;
        double r61763 = r61761 + r61762;
        double r61764 = 1.0;
        double r61765 = a;
        double r61766 = r61751 + r61765;
        double r61767 = r61766 * r61751;
        double r61768 = b;
        double r61769 = r61767 + r61768;
        double r61770 = r61769 * r61751;
        double r61771 = c;
        double r61772 = r61770 + r61771;
        double r61773 = r61772 * r61751;
        double r61774 = i;
        double r61775 = r61773 + r61774;
        double r61776 = r61764 / r61775;
        double r61777 = r61763 * r61776;
        return r61777;
}

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. Using strategy rm

  3. Applied div-inv29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2019352 
(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)))