Average Error: 4.0 → 2.8
Time: 13.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.13489987273627684 \cdot 10^{-234} \lor \neg \left(t \le 4.0260572358084834 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -3.13489987273627684 \cdot 10^{-234} \lor \neg \left(t \le 4.0260572358084834 \cdot 10^{-181}\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 \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \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)}{t \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 r105676 = x;
        double r105677 = y;
        double r105678 = 2.0;
        double r105679 = z;
        double r105680 = t;
        double r105681 = a;
        double r105682 = r105680 + r105681;
        double r105683 = sqrt(r105682);
        double r105684 = r105679 * r105683;
        double r105685 = r105684 / r105680;
        double r105686 = b;
        double r105687 = c;
        double r105688 = r105686 - r105687;
        double r105689 = 5.0;
        double r105690 = 6.0;
        double r105691 = r105689 / r105690;
        double r105692 = r105681 + r105691;
        double r105693 = 3.0;
        double r105694 = r105680 * r105693;
        double r105695 = r105678 / r105694;
        double r105696 = r105692 - r105695;
        double r105697 = r105688 * r105696;
        double r105698 = r105685 - r105697;
        double r105699 = r105678 * r105698;
        double r105700 = exp(r105699);
        double r105701 = r105677 * r105700;
        double r105702 = r105676 + r105701;
        double r105703 = r105676 / r105702;
        return r105703;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r105704 = t;
        double r105705 = -3.134899872736277e-234;
        bool r105706 = r105704 <= r105705;
        double r105707 = 4.0260572358084834e-181;
        bool r105708 = r105704 <= r105707;
        double r105709 = !r105708;
        bool r105710 = r105706 || r105709;
        double r105711 = x;
        double r105712 = y;
        double r105713 = 2.0;
        double r105714 = z;
        double r105715 = cbrt(r105704);
        double r105716 = r105715 * r105715;
        double r105717 = r105714 / r105716;
        double r105718 = a;
        double r105719 = r105704 + r105718;
        double r105720 = sqrt(r105719);
        double r105721 = r105720 / r105715;
        double r105722 = r105717 * r105721;
        double r105723 = b;
        double r105724 = c;
        double r105725 = r105723 - r105724;
        double r105726 = 5.0;
        double r105727 = 6.0;
        double r105728 = r105726 / r105727;
        double r105729 = r105718 + r105728;
        double r105730 = 3.0;
        double r105731 = r105704 * r105730;
        double r105732 = r105713 / r105731;
        double r105733 = r105729 - r105732;
        double r105734 = r105725 * r105733;
        double r105735 = r105722 - r105734;
        double r105736 = r105713 * r105735;
        double r105737 = exp(r105736);
        double r105738 = r105712 * r105737;
        double r105739 = r105711 + r105738;
        double r105740 = r105711 / r105739;
        double r105741 = r105714 * r105720;
        double r105742 = r105718 - r105728;
        double r105743 = r105742 * r105731;
        double r105744 = r105741 * r105743;
        double r105745 = r105718 * r105718;
        double r105746 = r105728 * r105728;
        double r105747 = r105745 - r105746;
        double r105748 = r105747 * r105731;
        double r105749 = r105742 * r105713;
        double r105750 = r105748 - r105749;
        double r105751 = r105725 * r105750;
        double r105752 = r105704 * r105751;
        double r105753 = r105744 - r105752;
        double r105754 = r105704 * r105743;
        double r105755 = r105753 / r105754;
        double r105756 = r105713 * r105755;
        double r105757 = exp(r105756);
        double r105758 = r105712 * r105757;
        double r105759 = r105711 + r105758;
        double r105760 = r105711 / r105759;
        double r105761 = r105710 ? r105740 : r105760;
        return r105761;
}

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 < -3.134899872736277e-234 or 4.0260572358084834e-181 < t

    1. Initial program 2.8

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

    3. Applied add-cube-cbrt2.8

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

    4. Applied times-frac1.3

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

    if -3.134899872736277e-234 < t < 4.0260572358084834e-181

    1. Initial program 9.6

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

    3. Applied flip-+13.8

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

    4. Applied frac-sub13.8

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

    5. Applied associate-*r/13.8

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

    6. Applied frac-sub9.6

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.13489987273627684 \cdot 10^{-234} \lor \neg \left(t \le 4.0260572358084834 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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)))))))))))