Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Average Error: 2.0 → 0.7

Time: 25.9s

Precision: 64

Math

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

↓

\[\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\right)\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r541556 = x;
        double r541557 = y;
        double r541558 = z;
        double r541559 = log(r541558);
        double r541560 = r541557 * r541559;
        double r541561 = t;
        double r541562 = 1.0;
        double r541563 = r541561 - r541562;
        double r541564 = a;
        double r541565 = log(r541564);
        double r541566 = r541563 * r541565;
        double r541567 = r541560 + r541566;
        double r541568 = b;
        double r541569 = r541567 - r541568;
        double r541570 = exp(r541569);
        double r541571 = r541556 * r541570;
        double r541572 = r541571 / r541557;
        return r541572;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r541573 = 1.0;
        double r541574 = sqrt(r541573);
        double r541575 = sqrt(r541574);
        double r541576 = a;
        double r541577 = cbrt(r541576);
        double r541578 = r541577 * r541577;
        double r541579 = sqrt(r541578);
        double r541580 = r541575 / r541579;
        double r541581 = 1.0;
        double r541582 = pow(r541580, r541581);
        double r541583 = y;
        double r541584 = z;
        double r541585 = r541573 / r541584;
        double r541586 = log(r541585);
        double r541587 = r541583 * r541586;
        double r541588 = r541573 / r541576;
        double r541589 = log(r541588);
        double r541590 = t;
        double r541591 = r541589 * r541590;
        double r541592 = b;
        double r541593 = r541591 + r541592;
        double r541594 = r541587 + r541593;
        double r541595 = exp(r541594);
        double r541596 = sqrt(r541595);
        double r541597 = cbrt(r541596);
        double r541598 = r541597 * r541597;
        double r541599 = r541582 / r541598;
        double r541600 = cbrt(r541583);
        double r541601 = r541600 * r541600;
        double r541602 = r541599 / r541601;
        double r541603 = sqrt(r541577);
        double r541604 = r541575 / r541603;
        double r541605 = pow(r541604, r541581);
        double r541606 = r541605 / r541597;
        double r541607 = r541606 / r541600;
        double r541608 = sqrt(r541576);
        double r541609 = r541574 / r541608;
        double r541610 = pow(r541609, r541581);
        double r541611 = r541610 / r541596;
        double r541612 = x;
        double r541613 = r541611 * r541612;
        double r541614 = r541607 * r541613;
        double r541615 = r541602 * r541614;
        return r541615;
}

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

Target

Original	2.0
Target	11.5
Herbie	0.7

\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

1. Initial program 2.0

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

2. Taylor expanded around inf 2.0

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

3. Simplified 6.2

   \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}}\]
4. Using strategy rm

5. Applied div-inv 6.2

   \[\leadsto \frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\color{blue}{y \cdot \frac{1}{x}}}\]

6. Applied add-sqr-sqrt 6.2

   \[\leadsto \frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{\color{blue}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{y \cdot \frac{1}{x}}\]

7. Applied add-sqr-sqrt 6.2

   \[\leadsto \frac{\frac{{\left(\frac{1}{\color{blue}{\sqrt{a} \cdot \sqrt{a}}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y \cdot \frac{1}{x}}\]

8. Applied add-sqr-sqrt 6.2

   \[\leadsto \frac{\frac{{\left(\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\sqrt{a} \cdot \sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y \cdot \frac{1}{x}}\]

9. Applied times-frac 6.2

   \[\leadsto \frac{\frac{{\color{blue}{\left(\frac{\sqrt{1}}{\sqrt{a}} \cdot \frac{\sqrt{1}}{\sqrt{a}}\right)}}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y \cdot \frac{1}{x}}\]

10. Applied unpow-prod-down 6.2

    \[\leadsto \frac{\frac{\color{blue}{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1} \cdot {\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y \cdot \frac{1}{x}}\]

11. Applied times-frac 6.2

    \[\leadsto \frac{\color{blue}{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{y \cdot \frac{1}{x}}\]

12. Applied times-frac 1.0

    \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y} \cdot \frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\frac{1}{x}}}\]

13. Simplified 1.0

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y} \cdot \color{blue}{\left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)}\]
14. Using strategy rm

15. Applied add-cube-cbrt 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

16. Applied add-cube-cbrt 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\color{blue}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

17. Applied add-cube-cbrt 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}}\right)}^{1}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

18. Applied sqrt-prod 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{1}}{\color{blue}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt{\sqrt[3]{a}}}}\right)}^{1}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

19. Applied add-sqr-sqrt 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt{\sqrt[3]{a}}}\right)}^{1}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

20. Applied sqrt-prod 1.2

    \[\leadsto \frac{\frac{{\left(\frac{\color{blue}{\sqrt{\sqrt{1}} \cdot \sqrt{\sqrt{1}}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt{\sqrt[3]{a}}}\right)}^{1}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

21. Applied times-frac 1.2

    \[\leadsto \frac{\frac{{\color{blue}{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}}^{1}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

22. Applied unpow-prod-down 1.2

    \[\leadsto \frac{\frac{\color{blue}{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1} \cdot {\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}}{\left(\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

23. Applied times-frac 1.2

    \[\leadsto \frac{\color{blue}{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}} \cdot \frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

24. Applied times-frac 1.2

    \[\leadsto \color{blue}{\left(\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}}\right)} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\]

25. Applied associate-*l* 0.7

    \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\right)}\]

26. Final simplification 0.7

    \[\leadsto \frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a} \cdot \sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\frac{{\left(\frac{\sqrt{\sqrt{1}}}{\sqrt{\sqrt[3]{a}}}\right)}^{1}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}} \cdot \left(\frac{{\left(\frac{\sqrt{1}}{\sqrt{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))