Average Error: 29.1 → 29.2
Time: 9.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61649 = x;
        double r61650 = y;
        double r61651 = r61649 * r61650;
        double r61652 = z;
        double r61653 = r61651 + r61652;
        double r61654 = r61653 * r61650;
        double r61655 = 27464.7644705;
        double r61656 = r61654 + r61655;
        double r61657 = r61656 * r61650;
        double r61658 = 230661.510616;
        double r61659 = r61657 + r61658;
        double r61660 = r61659 * r61650;
        double r61661 = t;
        double r61662 = r61660 + r61661;
        double r61663 = a;
        double r61664 = r61650 + r61663;
        double r61665 = r61664 * r61650;
        double r61666 = b;
        double r61667 = r61665 + r61666;
        double r61668 = r61667 * r61650;
        double r61669 = c;
        double r61670 = r61668 + r61669;
        double r61671 = r61670 * r61650;
        double r61672 = i;
        double r61673 = r61671 + r61672;
        double r61674 = r61662 / r61673;
        return r61674;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61675 = x;
        double r61676 = y;
        double r61677 = r61675 * r61676;
        double r61678 = z;
        double r61679 = r61677 + r61678;
        double r61680 = r61679 * r61676;
        double r61681 = 27464.7644705;
        double r61682 = r61680 + r61681;
        double r61683 = r61682 * r61676;
        double r61684 = 230661.510616;
        double r61685 = r61683 + r61684;
        double r61686 = r61685 * r61676;
        double r61687 = t;
        double r61688 = r61686 + r61687;
        double r61689 = a;
        double r61690 = r61676 + r61689;
        double r61691 = r61690 * r61676;
        double r61692 = b;
        double r61693 = r61691 + r61692;
        double r61694 = cbrt(r61693);
        double r61695 = r61694 * r61694;
        double r61696 = r61694 * r61676;
        double r61697 = r61695 * r61696;
        double r61698 = c;
        double r61699 = r61697 + r61698;
        double r61700 = r61699 * r61676;
        double r61701 = i;
        double r61702 = r61700 + r61701;
        double r61703 = r61688 / r61702;
        return r61703;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020083 +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)))