Average Error: 28.7 → 28.8
Time: 30.1s
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 r65660 = x;
        double r65661 = y;
        double r65662 = r65660 * r65661;
        double r65663 = z;
        double r65664 = r65662 + r65663;
        double r65665 = r65664 * r65661;
        double r65666 = 27464.7644705;
        double r65667 = r65665 + r65666;
        double r65668 = r65667 * r65661;
        double r65669 = 230661.510616;
        double r65670 = r65668 + r65669;
        double r65671 = r65670 * r65661;
        double r65672 = t;
        double r65673 = r65671 + r65672;
        double r65674 = a;
        double r65675 = r65661 + r65674;
        double r65676 = r65675 * r65661;
        double r65677 = b;
        double r65678 = r65676 + r65677;
        double r65679 = r65678 * r65661;
        double r65680 = c;
        double r65681 = r65679 + r65680;
        double r65682 = r65681 * r65661;
        double r65683 = i;
        double r65684 = r65682 + r65683;
        double r65685 = r65673 / r65684;
        return r65685;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65686 = x;
        double r65687 = y;
        double r65688 = r65686 * r65687;
        double r65689 = z;
        double r65690 = r65688 + r65689;
        double r65691 = r65690 * r65687;
        double r65692 = 27464.7644705;
        double r65693 = r65691 + r65692;
        double r65694 = r65693 * r65687;
        double r65695 = 230661.510616;
        double r65696 = r65694 + r65695;
        double r65697 = r65696 * r65687;
        double r65698 = t;
        double r65699 = r65697 + r65698;
        double r65700 = 1.0;
        double r65701 = a;
        double r65702 = r65687 + r65701;
        double r65703 = r65702 * r65687;
        double r65704 = b;
        double r65705 = r65703 + r65704;
        double r65706 = r65705 * r65687;
        double r65707 = c;
        double r65708 = r65706 + r65707;
        double r65709 = r65708 * r65687;
        double r65710 = i;
        double r65711 = r65709 + r65710;
        double r65712 = r65700 / r65711;
        double r65713 = r65699 * r65712;
        return r65713;
}

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)))