Average Error: 29.2 → 29.3
Time: 10.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\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{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\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 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 = a;
        double r65701 = r65687 + r65700;
        double r65702 = r65701 * r65687;
        double r65703 = b;
        double r65704 = r65702 + r65703;
        double r65705 = r65704 * r65687;
        double r65706 = c;
        double r65707 = r65705 + r65706;
        double r65708 = r65707 * r65687;
        double r65709 = i;
        double r65710 = r65708 + r65709;
        double r65711 = r65699 / r65710;
        return r65711;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65712 = x;
        double r65713 = y;
        double r65714 = r65712 * r65713;
        double r65715 = z;
        double r65716 = r65714 + r65715;
        double r65717 = r65716 * r65713;
        double r65718 = 27464.7644705;
        double r65719 = r65717 + r65718;
        double r65720 = cbrt(r65713);
        double r65721 = r65720 * r65720;
        double r65722 = r65719 * r65721;
        double r65723 = r65722 * r65720;
        double r65724 = 230661.510616;
        double r65725 = r65723 + r65724;
        double r65726 = r65725 * r65713;
        double r65727 = t;
        double r65728 = r65726 + r65727;
        double r65729 = a;
        double r65730 = r65713 + r65729;
        double r65731 = r65730 * r65713;
        double r65732 = b;
        double r65733 = r65731 + r65732;
        double r65734 = r65733 * r65713;
        double r65735 = c;
        double r65736 = r65734 + r65735;
        double r65737 = r65736 * r65713;
        double r65738 = i;
        double r65739 = r65737 + r65738;
        double r65740 = r65728 / r65739;
        return r65740;
}

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 add-cube-cbrt29.3

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

  4. Applied associate-*r*29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019354 
(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)))