Average Error: 28.8 → 28.9
Time: 7.6s
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 r65652 = x;
        double r65653 = y;
        double r65654 = r65652 * r65653;
        double r65655 = z;
        double r65656 = r65654 + r65655;
        double r65657 = r65656 * r65653;
        double r65658 = 27464.7644705;
        double r65659 = r65657 + r65658;
        double r65660 = r65659 * r65653;
        double r65661 = 230661.510616;
        double r65662 = r65660 + r65661;
        double r65663 = r65662 * r65653;
        double r65664 = t;
        double r65665 = r65663 + r65664;
        double r65666 = a;
        double r65667 = r65653 + r65666;
        double r65668 = r65667 * r65653;
        double r65669 = b;
        double r65670 = r65668 + r65669;
        double r65671 = r65670 * r65653;
        double r65672 = c;
        double r65673 = r65671 + r65672;
        double r65674 = r65673 * r65653;
        double r65675 = i;
        double r65676 = r65674 + r65675;
        double r65677 = r65665 / r65676;
        return r65677;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65678 = x;
        double r65679 = y;
        double r65680 = r65678 * r65679;
        double r65681 = z;
        double r65682 = r65680 + r65681;
        double r65683 = cbrt(r65682);
        double r65684 = r65683 * r65683;
        double r65685 = r65683 * r65679;
        double r65686 = r65684 * r65685;
        double r65687 = 27464.7644705;
        double r65688 = r65686 + r65687;
        double r65689 = r65688 * r65679;
        double r65690 = 230661.510616;
        double r65691 = r65689 + r65690;
        double r65692 = r65691 * r65679;
        double r65693 = t;
        double r65694 = r65692 + r65693;
        double r65695 = 1.0;
        double r65696 = a;
        double r65697 = r65679 + r65696;
        double r65698 = r65697 * r65679;
        double r65699 = b;
        double r65700 = r65698 + r65699;
        double r65701 = r65700 * r65679;
        double r65702 = c;
        double r65703 = r65701 + r65702;
        double r65704 = r65703 * r65679;
        double r65705 = i;
        double r65706 = r65704 + r65705;
        double r65707 = r65695 / r65706;
        double r65708 = r65694 * r65707;
        return r65708;
}

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)))