Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2

Average Error: 3.8 → 3.4

Time: 18.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -6.55961936279920487 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\left(1 \cdot \left(a \cdot c\right) + 0.83333333333333337 \cdot c\right) - 1 \cdot \left(a \cdot b\right)}\right)}}\\ \mathbf{elif}\;t \le 5.7825904422029032 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r119635 = x;
        double r119636 = y;
        double r119637 = 2.0;
        double r119638 = z;
        double r119639 = t;
        double r119640 = a;
        double r119641 = r119639 + r119640;
        double r119642 = sqrt(r119641);
        double r119643 = r119638 * r119642;
        double r119644 = r119643 / r119639;
        double r119645 = b;
        double r119646 = c;
        double r119647 = r119645 - r119646;
        double r119648 = 5.0;
        double r119649 = 6.0;
        double r119650 = r119648 / r119649;
        double r119651 = r119640 + r119650;
        double r119652 = 3.0;
        double r119653 = r119639 * r119652;
        double r119654 = r119637 / r119653;
        double r119655 = r119651 - r119654;
        double r119656 = r119647 * r119655;
        double r119657 = r119644 - r119656;
        double r119658 = r119637 * r119657;
        double r119659 = exp(r119658);
        double r119660 = r119636 * r119659;
        double r119661 = r119635 + r119660;
        double r119662 = r119635 / r119661;
        return r119662;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r119663 = t;
        double r119664 = -6.559619362799205e-11;
        bool r119665 = r119663 <= r119664;
        double r119666 = x;
        double r119667 = y;
        double r119668 = 2.0;
        double r119669 = 1.0;
        double r119670 = a;
        double r119671 = c;
        double r119672 = r119670 * r119671;
        double r119673 = r119669 * r119672;
        double r119674 = 0.8333333333333334;
        double r119675 = r119674 * r119671;
        double r119676 = r119673 + r119675;
        double r119677 = b;
        double r119678 = r119670 * r119677;
        double r119679 = r119669 * r119678;
        double r119680 = r119676 - r119679;
        double r119681 = exp(r119680);
        double r119682 = log(r119681);
        double r119683 = r119668 * r119682;
        double r119684 = exp(r119683);
        double r119685 = r119667 * r119684;
        double r119686 = r119666 + r119685;
        double r119687 = r119666 / r119686;
        double r119688 = 5.782590442202903e-125;
        bool r119689 = r119663 <= r119688;
        double r119690 = z;
        double r119691 = r119663 + r119670;
        double r119692 = sqrt(r119691);
        double r119693 = cbrt(r119663);
        double r119694 = r119692 / r119693;
        double r119695 = r119690 * r119694;
        double r119696 = 5.0;
        double r119697 = 6.0;
        double r119698 = r119696 / r119697;
        double r119699 = r119670 - r119698;
        double r119700 = 3.0;
        double r119701 = r119663 * r119700;
        double r119702 = r119699 * r119701;
        double r119703 = r119695 * r119702;
        double r119704 = r119693 * r119693;
        double r119705 = r119677 - r119671;
        double r119706 = r119670 * r119670;
        double r119707 = r119698 * r119698;
        double r119708 = r119706 - r119707;
        double r119709 = r119708 * r119701;
        double r119710 = r119699 * r119668;
        double r119711 = r119709 - r119710;
        double r119712 = r119705 * r119711;
        double r119713 = r119704 * r119712;
        double r119714 = r119703 - r119713;
        double r119715 = r119704 * r119702;
        double r119716 = r119714 / r119715;
        double r119717 = exp(r119716);
        double r119718 = log(r119717);
        double r119719 = r119668 * r119718;
        double r119720 = exp(r119719);
        double r119721 = r119667 * r119720;
        double r119722 = r119666 + r119721;
        double r119723 = r119666 / r119722;
        double r119724 = r119690 / r119704;
        double r119725 = r119724 * r119694;
        double r119726 = r119670 + r119698;
        double r119727 = r119668 / r119701;
        double r119728 = r119726 - r119727;
        double r119729 = r119705 * r119728;
        double r119730 = r119725 - r119729;
        double r119731 = exp(r119730);
        double r119732 = log(r119731);
        double r119733 = r119668 * r119732;
        double r119734 = exp(r119733);
        double r119735 = r119667 * r119734;
        double r119736 = r119666 + r119735;
        double r119737 = r119666 / r119736;
        double r119738 = r119689 ? r119723 : r119737;
        double r119739 = r119665 ? r119687 : r119738;
        return r119739;
}

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

Derivation

1. Split input into 3 regimes

2. if t < -6.559619362799205e-11

   1. Initial program 3.4

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

   3. Applied add-cube-cbrt 3.4

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

   4. Applied times-frac 0.6

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

   6. Applied add-log-exp 3.0

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

   7. Applied add-log-exp 16.0

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

   8. Applied diff-log 16.0

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

   9. Simplified 0.6

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

   11. Applied flip-+ 2.2

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

   12. Applied frac-sub 30.3

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

   13. Applied associate-*r/ 30.9

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

   14. Applied associate-*l/ 31.6

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

   15. Applied frac-sub 40.3

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

   16. Taylor expanded around inf 7.7

       \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\color{blue}{\left(1 \cdot \left(a \cdot c\right) + 0.83333333333333337 \cdot c\right) - 1 \cdot \left(a \cdot b\right)}}\right)}}\]

   if -6.559619362799205e-11 < t < 5.782590442202903e-125

   1. Initial program 5.9

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

   3. Applied add-cube-cbrt 5.9

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

   4. Applied times-frac 6.0

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

   6. Applied add-log-exp 13.0

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

   7. Applied add-log-exp 24.7

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

   8. Applied diff-log 24.7

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

   9. Simplified 6.0

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

   11. Applied flip-+ 9.7

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

   12. Applied frac-sub 9.8

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

   13. Applied associate-*r/ 9.8

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

   14. Applied associate-*l/ 9.7

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

   15. Applied frac-sub 7.2

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

   if 5.782590442202903e-125 < t

   1. Initial program 2.6

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

   3. Applied add-cube-cbrt 2.6

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

   4. Applied times-frac 0.5

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

   6. Applied add-log-exp 3.6

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

   7. Applied add-log-exp 11.7

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

   8. Applied diff-log 11.7

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

   9. Simplified 0.5

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

4. Final simplification 3.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.55961936279920487 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\left(1 \cdot \left(a \cdot c\right) + 0.83333333333333337 \cdot c\right) - 1 \cdot \left(a \cdot b\right)}\right)}}\\ \mathbf{elif}\;t \le 5.7825904422029032 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 
(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)))))))))))