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

Average Error: 2.0 → 0.8

Time: 35.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r496916 = x;
        double r496917 = y;
        double r496918 = z;
        double r496919 = log(r496918);
        double r496920 = r496917 * r496919;
        double r496921 = t;
        double r496922 = 1.0;
        double r496923 = r496921 - r496922;
        double r496924 = a;
        double r496925 = log(r496924);
        double r496926 = r496923 * r496925;
        double r496927 = r496920 + r496926;
        double r496928 = b;
        double r496929 = r496927 - r496928;
        double r496930 = exp(r496929);
        double r496931 = r496916 * r496930;
        double r496932 = r496931 / r496917;
        return r496932;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r496933 = 1.0;
        double r496934 = cbrt(r496933);
        double r496935 = r496934 * r496934;
        double r496936 = a;
        double r496937 = cbrt(r496936);
        double r496938 = r496937 * r496937;
        double r496939 = r496935 / r496938;
        double r496940 = 1.0;
        double r496941 = pow(r496939, r496940);
        double r496942 = y;
        double r496943 = cbrt(r496942);
        double r496944 = r496943 * r496943;
        double r496945 = cbrt(r496935);
        double r496946 = sqrt(r496936);
        double r496947 = cbrt(r496946);
        double r496948 = r496945 / r496947;
        double r496949 = pow(r496948, r496940);
        double r496950 = z;
        double r496951 = r496933 / r496950;
        double r496952 = log(r496951);
        double r496953 = r496933 / r496936;
        double r496954 = log(r496953);
        double r496955 = t;
        double r496956 = b;
        double r496957 = fma(r496954, r496955, r496956);
        double r496958 = fma(r496942, r496952, r496957);
        double r496959 = exp(r496958);
        double r496960 = sqrt(r496959);
        double r496961 = r496949 / r496960;
        double r496962 = r496944 / r496961;
        double r496963 = r496933 / r496962;
        double r496964 = r496941 * r496963;
        double r496965 = x;
        double r496966 = cbrt(r496934);
        double r496967 = r496966 / r496947;
        double r496968 = pow(r496967, r496940);
        double r496969 = r496968 / r496960;
        double r496970 = r496943 / r496969;
        double r496971 = r496965 / r496970;
        double r496972 = r496964 * r496971;
        return r496972;
}

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	11.2
Herbie	0.8

\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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

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

3. Simplified 1.2

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

5. Applied associate-/l* 1.2

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\mathsf{fma}\left(y, \log \left(\frac{1}{z}\right), \mathsf{fma}\left(\log \left(\frac{1}{a}\right), t, b\right)\right)}}}}}\]
6. Using strategy rm

7. Applied *-un-lft-identity 1.2

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

8. Applied add-cube-cbrt 1.4

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

9. Applied add-cube-cbrt 1.4

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

10. Applied times-frac 1.4

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

11. Applied unpow-prod-down 1.4

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

12. Applied times-frac 1.4

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

13. Applied *-un-lft-identity 1.4

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

14. Applied times-frac 1.4

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

15. Applied *-un-lft-identity 1.4

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

16. Applied times-frac 1.1

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

17. Simplified 1.1

    \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}} \cdot \frac{x}{\frac{y}{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt[3]{a}}\right)}^{1}}{e^{\mathsf{fma}\left(y, \log \left(\frac{1}{z}\right), \mathsf{fma}\left(\log \left(\frac{1}{a}\right), t, b\right)\right)}}}}\]
18. Using strategy rm

19. Applied add-sqr-sqrt 1.1

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

20. Applied add-sqr-sqrt 1.1

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

21. Applied cbrt-prod 1.1

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

22. Applied add-cube-cbrt 1.1

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

23. Applied cbrt-prod 1.1

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

24. Applied times-frac 1.1

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

25. Applied unpow-prod-down 1.1

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

26. Applied times-frac 1.1

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

27. Applied add-cube-cbrt 1.1

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

28. Applied times-frac 1.1

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

29. Applied *-un-lft-identity 1.1

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

30. Applied times-frac 0.9

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

31. Applied associate-*r* 0.8

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

32. Final simplification 0.8

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))