Average Error: 29.1 → 29.2
Time: 29.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(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(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75639 = x;
        double r75640 = y;
        double r75641 = r75639 * r75640;
        double r75642 = z;
        double r75643 = r75641 + r75642;
        double r75644 = r75643 * r75640;
        double r75645 = 27464.7644705;
        double r75646 = r75644 + r75645;
        double r75647 = r75646 * r75640;
        double r75648 = 230661.510616;
        double r75649 = r75647 + r75648;
        double r75650 = r75649 * r75640;
        double r75651 = t;
        double r75652 = r75650 + r75651;
        double r75653 = a;
        double r75654 = r75640 + r75653;
        double r75655 = r75654 * r75640;
        double r75656 = b;
        double r75657 = r75655 + r75656;
        double r75658 = r75657 * r75640;
        double r75659 = c;
        double r75660 = r75658 + r75659;
        double r75661 = r75660 * r75640;
        double r75662 = i;
        double r75663 = r75661 + r75662;
        double r75664 = r75652 / r75663;
        return r75664;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75665 = x;
        double r75666 = y;
        double r75667 = r75665 * r75666;
        double r75668 = z;
        double r75669 = r75667 + r75668;
        double r75670 = r75669 * r75666;
        double r75671 = 27464.7644705;
        double r75672 = r75670 + r75671;
        double r75673 = r75672 * r75666;
        double r75674 = cbrt(r75673);
        double r75675 = r75674 * r75674;
        double r75676 = r75675 * r75674;
        double r75677 = 230661.510616;
        double r75678 = r75676 + r75677;
        double r75679 = r75678 * r75666;
        double r75680 = t;
        double r75681 = r75679 + r75680;
        double r75682 = a;
        double r75683 = r75666 + r75682;
        double r75684 = r75683 * r75666;
        double r75685 = b;
        double r75686 = r75684 + r75685;
        double r75687 = r75686 * r75666;
        double r75688 = c;
        double r75689 = r75687 + r75688;
        double r75690 = r75689 * r75666;
        double r75691 = i;
        double r75692 = r75690 + r75691;
        double r75693 = r75681 / r75692;
        return r75693;
}

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

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 2019235 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))