Average Error: 28.8 → 28.9
Time: 8.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\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 + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69663 = x;
        double r69664 = y;
        double r69665 = r69663 * r69664;
        double r69666 = z;
        double r69667 = r69665 + r69666;
        double r69668 = r69667 * r69664;
        double r69669 = 27464.7644705;
        double r69670 = r69668 + r69669;
        double r69671 = r69670 * r69664;
        double r69672 = 230661.510616;
        double r69673 = r69671 + r69672;
        double r69674 = r69673 * r69664;
        double r69675 = t;
        double r69676 = r69674 + r69675;
        double r69677 = a;
        double r69678 = r69664 + r69677;
        double r69679 = r69678 * r69664;
        double r69680 = b;
        double r69681 = r69679 + r69680;
        double r69682 = r69681 * r69664;
        double r69683 = c;
        double r69684 = r69682 + r69683;
        double r69685 = r69684 * r69664;
        double r69686 = i;
        double r69687 = r69685 + r69686;
        double r69688 = r69676 / r69687;
        return r69688;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69689 = x;
        double r69690 = y;
        double r69691 = r69689 * r69690;
        double r69692 = z;
        double r69693 = r69691 + r69692;
        double r69694 = r69693 * r69690;
        double r69695 = 27464.7644705;
        double r69696 = r69694 + r69695;
        double r69697 = r69696 * r69690;
        double r69698 = cbrt(r69697);
        double r69699 = r69698 * r69698;
        double r69700 = r69699 * r69698;
        double r69701 = 230661.510616;
        double r69702 = r69700 + r69701;
        double r69703 = r69702 * r69690;
        double r69704 = t;
        double r69705 = r69703 + r69704;
        double r69706 = a;
        double r69707 = r69690 + r69706;
        double r69708 = r69707 * r69690;
        double r69709 = b;
        double r69710 = r69708 + r69709;
        double r69711 = r69710 * r69690;
        double r69712 = c;
        double r69713 = r69711 + r69712;
        double r69714 = r69713 * r69690;
        double r69715 = i;
        double r69716 = r69714 + r69715;
        double r69717 = r69705 / r69716;
        return r69717;
}

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 28.8

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

  3. Applied add-cube-cbrt28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2020018 +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)))