Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2

Average Error: 2.0 → 0.8

Time: 35.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r174050 = x;
        double r174051 = y;
        double r174052 = z;
        double r174053 = log(r174052);
        double r174054 = r174051 * r174053;
        double r174055 = t;
        double r174056 = 1.0;
        double r174057 = r174055 - r174056;
        double r174058 = a;
        double r174059 = log(r174058);
        double r174060 = r174057 * r174059;
        double r174061 = r174054 + r174060;
        double r174062 = b;
        double r174063 = r174061 - r174062;
        double r174064 = exp(r174063);
        double r174065 = r174050 * r174064;
        double r174066 = r174065 / r174051;
        return r174066;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r174067 = 1.0;
        double r174068 = cbrt(r174067);
        double r174069 = r174068 * r174068;
        double r174070 = a;
        double r174071 = cbrt(r174070);
        double r174072 = r174071 * r174071;
        double r174073 = r174069 / r174072;
        double r174074 = 1.0;
        double r174075 = pow(r174073, r174074);
        double r174076 = y;
        double r174077 = cbrt(r174076);
        double r174078 = r174077 * r174077;
        double r174079 = sqrt(r174070);
        double r174080 = cbrt(r174079);
        double r174081 = r174068 / r174080;
        double r174082 = pow(r174081, r174074);
        double r174083 = z;
        double r174084 = r174067 / r174083;
        double r174085 = log(r174084);
        double r174086 = r174067 / r174070;
        double r174087 = log(r174086);
        double r174088 = t;
        double r174089 = b;
        double r174090 = fma(r174087, r174088, r174089);
        double r174091 = fma(r174076, r174085, r174090);
        double r174092 = exp(r174091);
        double r174093 = sqrt(r174092);
        double r174094 = r174082 / r174093;
        double r174095 = r174078 / r174094;
        double r174096 = r174067 / r174095;
        double r174097 = r174075 * r174096;
        double r174098 = x;
        double r174099 = r174077 / r174094;
        double r174100 = r174098 / r174099;
        double r174101 = r174097 * r174100;
        return r174101;
}

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

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 *-un-lft-identity 1.1

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

23. Applied cbrt-prod 1.1

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

24. Applied times-frac 1.1

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

25. Applied unpow-prod-down 1.1

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

26. Applied times-frac 1.1

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

27. Applied add-cube-cbrt 1.1

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

28. Applied times-frac 1.1

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

29. Applied *-un-lft-identity 1.1

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

30. Applied times-frac 0.9

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

31. Applied associate-*r* 0.8

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

32. Final simplification 0.8

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

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"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))