Average Error: 1.9 → 1.0
Time: 17.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{{\left(\sqrt{\frac{1}{a}}\right)}^{\left(2 \cdot 1\right)}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}} \cdot \frac{1}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{{\left(\sqrt{\frac{1}{a}}\right)}^{\left(2 \cdot 1\right)}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}} \cdot \frac{1}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r80877 = x;
        double r80878 = y;
        double r80879 = z;
        double r80880 = log(r80879);
        double r80881 = r80878 * r80880;
        double r80882 = t;
        double r80883 = 1.0;
        double r80884 = r80882 - r80883;
        double r80885 = a;
        double r80886 = log(r80885);
        double r80887 = r80884 * r80886;
        double r80888 = r80881 + r80887;
        double r80889 = b;
        double r80890 = r80888 - r80889;
        double r80891 = exp(r80890);
        double r80892 = r80877 * r80891;
        double r80893 = r80892 / r80878;
        return r80893;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r80894 = x;
        double r80895 = y;
        double r80896 = cbrt(r80895);
        double r80897 = r80896 * r80896;
        double r80898 = 1.0;
        double r80899 = a;
        double r80900 = r80898 / r80899;
        double r80901 = sqrt(r80900);
        double r80902 = 2.0;
        double r80903 = 1.0;
        double r80904 = r80902 * r80903;
        double r80905 = pow(r80901, r80904);
        double r80906 = z;
        double r80907 = r80898 / r80906;
        double r80908 = log(r80907);
        double r80909 = r80895 * r80908;
        double r80910 = log(r80900);
        double r80911 = t;
        double r80912 = r80910 * r80911;
        double r80913 = b;
        double r80914 = r80912 + r80913;
        double r80915 = r80909 + r80914;
        double r80916 = exp(r80915);
        double r80917 = cbrt(r80916);
        double r80918 = r80917 * r80917;
        double r80919 = r80905 / r80918;
        double r80920 = r80919 / r80917;
        double r80921 = r80897 / r80920;
        double r80922 = r80894 / r80921;
        double r80923 = r80898 / r80896;
        double r80924 = r80922 * r80923;
        return r80924;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified1.3

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

  5. Applied div-inv1.3

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

  7. Applied add-cube-cbrt1.3

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

  8. Applied add-sqr-sqrt1.3

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

  9. Applied unpow-prod-down1.3

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

  10. Applied times-frac1.3

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

  11. Applied associate-*r*1.3

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

  13. Applied add-cube-cbrt1.4

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

  14. Applied *-un-lft-identity1.4

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

  15. Applied times-frac1.4

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

  16. Applied associate-*r*1.4

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

  17. Simplified1.0

    \[\leadsto \color{blue}{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{{\left(\sqrt{\frac{1}{a}}\right)}^{\left(2 \cdot 1\right)}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}} \cdot \frac{1}{\sqrt[3]{y}}\]

  18. Final simplification1.0

    \[\leadsto \frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\frac{{\left(\sqrt{\frac{1}{a}}\right)}^{\left(2 \cdot 1\right)}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot \sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt[3]{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}} \cdot \frac{1}{\sqrt[3]{y}}\]

Reproduce

herbie shell --seed 2019362 
(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))