Average Error: 2.0 → 5.8
Time: 43.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.218811762387359090359297706344973358133 \cdot 10^{-281} \lor \neg \left(y \le 4.216998801399994992491902428717653999299 \cdot 10^{-137}\right):\\ \;\;\;\;{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \sqrt[3]{{\left(\frac{e^{\left(t \cdot \log a - b\right) + \log z \cdot y} \cdot x}{y}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{\frac{1}{{z}^{y}}}{\frac{\frac{{a}^{t}}{{a}^{1}}}{e^{b}}}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.218811762387359090359297706344973358133 \cdot 10^{-281} \lor \neg \left(y \le 4.216998801399994992491902428717653999299 \cdot 10^{-137}\right):\\
\;\;\;\;{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \sqrt[3]{{\left(\frac{e^{\left(t \cdot \log a - b\right) + \log z \cdot y} \cdot x}{y}\right)}^{3}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y \cdot \frac{\frac{1}{{z}^{y}}}{\frac{\frac{{a}^{t}}{{a}^{1}}}{e^{b}}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r75818 = x;
        double r75819 = y;
        double r75820 = z;
        double r75821 = log(r75820);
        double r75822 = r75819 * r75821;
        double r75823 = t;
        double r75824 = 1.0;
        double r75825 = r75823 - r75824;
        double r75826 = a;
        double r75827 = log(r75826);
        double r75828 = r75825 * r75827;
        double r75829 = r75822 + r75828;
        double r75830 = b;
        double r75831 = r75829 - r75830;
        double r75832 = exp(r75831);
        double r75833 = r75818 * r75832;
        double r75834 = r75833 / r75819;
        return r75834;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r75835 = y;
        double r75836 = -1.2188117623873591e-281;
        bool r75837 = r75835 <= r75836;
        double r75838 = 4.216998801399995e-137;
        bool r75839 = r75835 <= r75838;
        double r75840 = !r75839;
        bool r75841 = r75837 || r75840;
        double r75842 = 1.0;
        double r75843 = a;
        double r75844 = 1.0;
        double r75845 = pow(r75843, r75844);
        double r75846 = r75842 / r75845;
        double r75847 = pow(r75846, r75844);
        double r75848 = t;
        double r75849 = log(r75843);
        double r75850 = r75848 * r75849;
        double r75851 = b;
        double r75852 = r75850 - r75851;
        double r75853 = z;
        double r75854 = log(r75853);
        double r75855 = r75854 * r75835;
        double r75856 = r75852 + r75855;
        double r75857 = exp(r75856);
        double r75858 = x;
        double r75859 = r75857 * r75858;
        double r75860 = r75859 / r75835;
        double r75861 = 3.0;
        double r75862 = pow(r75860, r75861);
        double r75863 = cbrt(r75862);
        double r75864 = r75847 * r75863;
        double r75865 = pow(r75853, r75835);
        double r75866 = r75842 / r75865;
        double r75867 = pow(r75843, r75848);
        double r75868 = r75867 / r75845;
        double r75869 = exp(r75851);
        double r75870 = r75868 / r75869;
        double r75871 = r75866 / r75870;
        double r75872 = r75835 * r75871;
        double r75873 = r75858 / r75872;
        double r75874 = r75841 ? r75864 : r75873;
        return r75874;
}

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. Split input into 2 regimes

  2. if y < -1.2188117623873591e-281 or 4.216998801399995e-137 < y

    1. Initial program 1.6

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

    3. Applied associate-/l*1.4

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

    4. Simplified20.3

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

    6. Applied pow-sub20.3

      \[\leadsto \frac{x}{\frac{y}{{z}^{y} \cdot \frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{e^{b}}}}\]

    7. Taylor expanded around inf 20.5

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

    8. Simplified11.3

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

    10. Applied add-cbrt-cube11.3

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

    11. Applied add-cbrt-cube20.4

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

    12. Applied add-cbrt-cube35.5

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

    13. Applied cbrt-undiv36.7

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

    14. Applied cbrt-unprod36.7

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

    15. Simplified4.9

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

    if -1.2188117623873591e-281 < y < 4.216998801399995e-137

    1. Initial program 4.4

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

    3. Applied associate-/l*4.7

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

    4. Simplified10.8

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

    6. Applied pow-sub10.7

      \[\leadsto \frac{x}{\frac{y}{{z}^{y} \cdot \frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{e^{b}}}}\]
    7. Using strategy rm

    8. Applied div-inv10.7

      \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{{z}^{y} \cdot \frac{\frac{{a}^{t}}{{a}^{1}}}{e^{b}}}}}\]

    9. Simplified10.7

      \[\leadsto \frac{x}{y \cdot \color{blue}{\frac{\frac{1}{{z}^{y}}}{\frac{\frac{{a}^{t}}{{a}^{1}}}{e^{b}}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.218811762387359090359297706344973358133 \cdot 10^{-281} \lor \neg \left(y \le 4.216998801399994992491902428717653999299 \cdot 10^{-137}\right):\\ \;\;\;\;{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \sqrt[3]{{\left(\frac{e^{\left(t \cdot \log a - b\right) + \log z \cdot y} \cdot x}{y}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{\frac{1}{{z}^{y}}}{\frac{\frac{{a}^{t}}{{a}^{1}}}{e^{b}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))