Average Error: 29.1 → 29.2
Time: 8.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(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(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59677 = x;
        double r59678 = y;
        double r59679 = r59677 * r59678;
        double r59680 = z;
        double r59681 = r59679 + r59680;
        double r59682 = r59681 * r59678;
        double r59683 = 27464.7644705;
        double r59684 = r59682 + r59683;
        double r59685 = r59684 * r59678;
        double r59686 = 230661.510616;
        double r59687 = r59685 + r59686;
        double r59688 = r59687 * r59678;
        double r59689 = t;
        double r59690 = r59688 + r59689;
        double r59691 = a;
        double r59692 = r59678 + r59691;
        double r59693 = r59692 * r59678;
        double r59694 = b;
        double r59695 = r59693 + r59694;
        double r59696 = r59695 * r59678;
        double r59697 = c;
        double r59698 = r59696 + r59697;
        double r59699 = r59698 * r59678;
        double r59700 = i;
        double r59701 = r59699 + r59700;
        double r59702 = r59690 / r59701;
        return r59702;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59703 = x;
        double r59704 = y;
        double r59705 = r59703 * r59704;
        double r59706 = z;
        double r59707 = r59705 + r59706;
        double r59708 = cbrt(r59707);
        double r59709 = r59708 * r59708;
        double r59710 = r59708 * r59704;
        double r59711 = r59709 * r59710;
        double r59712 = 27464.7644705;
        double r59713 = r59711 + r59712;
        double r59714 = r59713 * r59704;
        double r59715 = 230661.510616;
        double r59716 = r59714 + r59715;
        double r59717 = r59716 * r59704;
        double r59718 = t;
        double r59719 = r59717 + r59718;
        double r59720 = a;
        double r59721 = r59704 + r59720;
        double r59722 = r59721 * r59704;
        double r59723 = b;
        double r59724 = r59722 + r59723;
        double r59725 = r59724 * r59704;
        double r59726 = c;
        double r59727 = r59725 + r59726;
        double r59728 = r59727 * r59704;
        double r59729 = i;
        double r59730 = r59728 + r59729;
        double r59731 = r59719 / r59730;
        return r59731;
}

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 29.1

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

  3. Applied add-cube-cbrt29.2

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

  4. Applied associate-*l*29.2

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

  5. Final simplification29.2

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(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)))