Average Error: 28.7 → 28.8
Time: 9.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot 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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91603 = x;
        double r91604 = y;
        double r91605 = r91603 * r91604;
        double r91606 = z;
        double r91607 = r91605 + r91606;
        double r91608 = r91607 * r91604;
        double r91609 = 27464.7644705;
        double r91610 = r91608 + r91609;
        double r91611 = r91610 * r91604;
        double r91612 = 230661.510616;
        double r91613 = r91611 + r91612;
        double r91614 = r91613 * r91604;
        double r91615 = t;
        double r91616 = r91614 + r91615;
        double r91617 = a;
        double r91618 = r91604 + r91617;
        double r91619 = r91618 * r91604;
        double r91620 = b;
        double r91621 = r91619 + r91620;
        double r91622 = r91621 * r91604;
        double r91623 = c;
        double r91624 = r91622 + r91623;
        double r91625 = r91624 * r91604;
        double r91626 = i;
        double r91627 = r91625 + r91626;
        double r91628 = r91616 / r91627;
        return r91628;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91629 = x;
        double r91630 = y;
        double r91631 = r91629 * r91630;
        double r91632 = z;
        double r91633 = r91631 + r91632;
        double r91634 = r91633 * r91630;
        double r91635 = 27464.7644705;
        double r91636 = r91634 + r91635;
        double r91637 = cbrt(r91636);
        double r91638 = r91637 * r91637;
        double r91639 = r91637 * r91630;
        double r91640 = r91638 * r91639;
        double r91641 = 230661.510616;
        double r91642 = r91640 + r91641;
        double r91643 = r91642 * r91630;
        double r91644 = t;
        double r91645 = r91643 + r91644;
        double r91646 = a;
        double r91647 = r91630 + r91646;
        double r91648 = r91647 * r91630;
        double r91649 = b;
        double r91650 = r91648 + r91649;
        double r91651 = r91650 * r91630;
        double r91652 = c;
        double r91653 = r91651 + r91652;
        double r91654 = r91653 * r91630;
        double r91655 = i;
        double r91656 = r91654 + r91655;
        double r91657 = r91645 / r91656;
        return r91657;
}

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 add-cube-cbrt28.8

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

  4. Applied associate-*l*28.8

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

  5. Final simplification28.8

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

Reproduce

herbie shell --seed 2019353 
(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)))