Average Error: 28.7 → 28.8
Time: 30.5s
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 r54685 = x;
        double r54686 = y;
        double r54687 = r54685 * r54686;
        double r54688 = z;
        double r54689 = r54687 + r54688;
        double r54690 = r54689 * r54686;
        double r54691 = 27464.7644705;
        double r54692 = r54690 + r54691;
        double r54693 = r54692 * r54686;
        double r54694 = 230661.510616;
        double r54695 = r54693 + r54694;
        double r54696 = r54695 * r54686;
        double r54697 = t;
        double r54698 = r54696 + r54697;
        double r54699 = a;
        double r54700 = r54686 + r54699;
        double r54701 = r54700 * r54686;
        double r54702 = b;
        double r54703 = r54701 + r54702;
        double r54704 = r54703 * r54686;
        double r54705 = c;
        double r54706 = r54704 + r54705;
        double r54707 = r54706 * r54686;
        double r54708 = i;
        double r54709 = r54707 + r54708;
        double r54710 = r54698 / r54709;
        return r54710;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r54711 = x;
        double r54712 = y;
        double r54713 = r54711 * r54712;
        double r54714 = z;
        double r54715 = r54713 + r54714;
        double r54716 = r54715 * r54712;
        double r54717 = 27464.7644705;
        double r54718 = r54716 + r54717;
        double r54719 = r54718 * r54712;
        double r54720 = 230661.510616;
        double r54721 = r54719 + r54720;
        double r54722 = r54721 * r54712;
        double r54723 = t;
        double r54724 = r54722 + r54723;
        double r54725 = 1.0;
        double r54726 = a;
        double r54727 = r54712 + r54726;
        double r54728 = r54727 * r54712;
        double r54729 = b;
        double r54730 = r54728 + r54729;
        double r54731 = r54730 * r54712;
        double r54732 = c;
        double r54733 = r54731 + r54732;
        double r54734 = r54733 * r54712;
        double r54735 = i;
        double r54736 = r54734 + r54735;
        double r54737 = r54725 / r54736;
        double r54738 = r54724 * r54737;
        return r54738;
}

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 28.7

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

  3. Applied div-inv28.8

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

  4. Final simplification28.8

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

Reproduce

herbie shell --seed 2019323 
(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)))