Average Error: 28.7 → 28.8
Time: 16.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\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 r69649 = x;
        double r69650 = y;
        double r69651 = r69649 * r69650;
        double r69652 = z;
        double r69653 = r69651 + r69652;
        double r69654 = r69653 * r69650;
        double r69655 = 27464.7644705;
        double r69656 = r69654 + r69655;
        double r69657 = r69656 * r69650;
        double r69658 = 230661.510616;
        double r69659 = r69657 + r69658;
        double r69660 = r69659 * r69650;
        double r69661 = t;
        double r69662 = r69660 + r69661;
        double r69663 = a;
        double r69664 = r69650 + r69663;
        double r69665 = r69664 * r69650;
        double r69666 = b;
        double r69667 = r69665 + r69666;
        double r69668 = r69667 * r69650;
        double r69669 = c;
        double r69670 = r69668 + r69669;
        double r69671 = r69670 * r69650;
        double r69672 = i;
        double r69673 = r69671 + r69672;
        double r69674 = r69662 / r69673;
        return r69674;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69675 = x;
        double r69676 = y;
        double r69677 = r69675 * r69676;
        double r69678 = z;
        double r69679 = r69677 + r69678;
        double r69680 = r69679 * r69676;
        double r69681 = 27464.7644705;
        double r69682 = r69680 + r69681;
        double r69683 = r69682 * r69676;
        double r69684 = 230661.510616;
        double r69685 = r69683 + r69684;
        double r69686 = r69685 * r69676;
        double r69687 = t;
        double r69688 = r69686 + r69687;
        double r69689 = 1.0;
        double r69690 = b;
        double r69691 = r69676 * r69690;
        double r69692 = 3.0;
        double r69693 = pow(r69676, r69692);
        double r69694 = a;
        double r69695 = 2.0;
        double r69696 = pow(r69676, r69695);
        double r69697 = r69694 * r69696;
        double r69698 = r69693 + r69697;
        double r69699 = r69691 + r69698;
        double r69700 = c;
        double r69701 = r69699 + r69700;
        double r69702 = r69701 * r69676;
        double r69703 = i;
        double r69704 = r69702 + r69703;
        double r69705 = r69689 / r69704;
        double r69706 = r69688 * r69705;
        return r69706;
}

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

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

  2. Taylor expanded around inf 28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020047 
(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)))