Average Error: 28.8 → 28.9
Time: 7.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\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 r69687 = x;
        double r69688 = y;
        double r69689 = r69687 * r69688;
        double r69690 = z;
        double r69691 = r69689 + r69690;
        double r69692 = r69691 * r69688;
        double r69693 = 27464.7644705;
        double r69694 = r69692 + r69693;
        double r69695 = r69694 * r69688;
        double r69696 = 230661.510616;
        double r69697 = r69695 + r69696;
        double r69698 = r69697 * r69688;
        double r69699 = t;
        double r69700 = r69698 + r69699;
        double r69701 = a;
        double r69702 = r69688 + r69701;
        double r69703 = r69702 * r69688;
        double r69704 = b;
        double r69705 = r69703 + r69704;
        double r69706 = r69705 * r69688;
        double r69707 = c;
        double r69708 = r69706 + r69707;
        double r69709 = r69708 * r69688;
        double r69710 = i;
        double r69711 = r69709 + r69710;
        double r69712 = r69700 / r69711;
        return r69712;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69713 = x;
        double r69714 = y;
        double r69715 = r69713 * r69714;
        double r69716 = z;
        double r69717 = r69715 + r69716;
        double r69718 = cbrt(r69717);
        double r69719 = r69718 * r69718;
        double r69720 = r69718 * r69714;
        double r69721 = r69719 * r69720;
        double r69722 = 27464.7644705;
        double r69723 = r69721 + r69722;
        double r69724 = r69723 * r69714;
        double r69725 = 230661.510616;
        double r69726 = r69724 + r69725;
        double r69727 = r69726 * r69714;
        double r69728 = t;
        double r69729 = r69727 + r69728;
        double r69730 = 1.0;
        double r69731 = a;
        double r69732 = r69714 + r69731;
        double r69733 = r69732 * r69714;
        double r69734 = b;
        double r69735 = r69733 + r69734;
        double r69736 = r69735 * r69714;
        double r69737 = c;
        double r69738 = r69736 + r69737;
        double r69739 = r69738 * r69714;
        double r69740 = i;
        double r69741 = r69739 + r69740;
        double r69742 = r69730 / r69741;
        double r69743 = r69729 * r69742;
        return r69743;
}

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 div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt28.9

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

  6. Applied associate-*l*28.9

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

  7. Final simplification28.9

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

Reproduce

herbie shell --seed 2020056 
(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)))