Average Error: 3.9 → 2.5
Time: 7.4s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.5493831176124007 \cdot 10^{-168} \lor \neg \left(t \le 7.95399199019938017 \cdot 10^{-200}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -6.5493831176124007 \cdot 10^{-168} \lor \neg \left(t \le 7.95399199019938017 \cdot 10^{-200}\right):\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r68700 = x;
        double r68701 = y;
        double r68702 = 2.0;
        double r68703 = z;
        double r68704 = t;
        double r68705 = a;
        double r68706 = r68704 + r68705;
        double r68707 = sqrt(r68706);
        double r68708 = r68703 * r68707;
        double r68709 = r68708 / r68704;
        double r68710 = b;
        double r68711 = c;
        double r68712 = r68710 - r68711;
        double r68713 = 5.0;
        double r68714 = 6.0;
        double r68715 = r68713 / r68714;
        double r68716 = r68705 + r68715;
        double r68717 = 3.0;
        double r68718 = r68704 * r68717;
        double r68719 = r68702 / r68718;
        double r68720 = r68716 - r68719;
        double r68721 = r68712 * r68720;
        double r68722 = r68709 - r68721;
        double r68723 = r68702 * r68722;
        double r68724 = exp(r68723);
        double r68725 = r68701 * r68724;
        double r68726 = r68700 + r68725;
        double r68727 = r68700 / r68726;
        return r68727;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r68728 = t;
        double r68729 = -6.549383117612401e-168;
        bool r68730 = r68728 <= r68729;
        double r68731 = 7.95399199019938e-200;
        bool r68732 = r68728 <= r68731;
        double r68733 = !r68732;
        bool r68734 = r68730 || r68733;
        double r68735 = x;
        double r68736 = y;
        double r68737 = 2.0;
        double r68738 = z;
        double r68739 = cbrt(r68728);
        double r68740 = r68739 * r68739;
        double r68741 = r68738 / r68740;
        double r68742 = a;
        double r68743 = r68728 + r68742;
        double r68744 = sqrt(r68743);
        double r68745 = r68744 / r68739;
        double r68746 = r68741 * r68745;
        double r68747 = b;
        double r68748 = c;
        double r68749 = r68747 - r68748;
        double r68750 = 5.0;
        double r68751 = 6.0;
        double r68752 = r68750 / r68751;
        double r68753 = r68742 + r68752;
        double r68754 = 3.0;
        double r68755 = r68728 * r68754;
        double r68756 = r68737 / r68755;
        double r68757 = r68753 - r68756;
        double r68758 = r68749 * r68757;
        double r68759 = r68746 - r68758;
        double r68760 = r68737 * r68759;
        double r68761 = exp(r68760);
        double r68762 = r68736 * r68761;
        double r68763 = r68735 + r68762;
        double r68764 = r68735 / r68763;
        double r68765 = r68738 * r68745;
        double r68766 = r68742 - r68752;
        double r68767 = r68766 * r68755;
        double r68768 = r68765 * r68767;
        double r68769 = r68742 * r68742;
        double r68770 = r68752 * r68752;
        double r68771 = r68769 - r68770;
        double r68772 = r68771 * r68755;
        double r68773 = r68766 * r68737;
        double r68774 = r68772 - r68773;
        double r68775 = r68749 * r68774;
        double r68776 = r68740 * r68775;
        double r68777 = r68768 - r68776;
        double r68778 = r68740 * r68767;
        double r68779 = r68777 / r68778;
        double r68780 = r68737 * r68779;
        double r68781 = exp(r68780);
        double r68782 = r68736 * r68781;
        double r68783 = r68735 + r68782;
        double r68784 = r68735 / r68783;
        double r68785 = r68734 ? r68764 : r68784;
        return r68785;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -6.549383117612401e-168 or 7.95399199019938e-200 < t

    1. Initial program 2.7

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt2.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied times-frac1.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    if -6.549383117612401e-168 < t < 7.95399199019938e-200

    1. Initial program 8.8

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt8.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied times-frac9.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    5. Using strategy rm

    6. Applied flip-+12.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5}{6} \cdot \frac{5}{6}}{a - \frac{5}{6}}} - \frac{2}{t \cdot 3}\right)\right)}}\]

    7. Applied frac-sub12.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    8. Applied associate-*r/12.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    9. Applied associate-*l/12.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} - \frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}\right)}}\]

    10. Applied frac-sub8.4

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.5493831176124007 \cdot 10^{-168} \lor \neg \left(t \le 7.95399199019938017 \cdot 10^{-200}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))