Average Error: 1.7 → 1.7
Time: 43.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}}\right)\right) \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}}}\right)\right) \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r3972856 = x;
        double r3972857 = y;
        double r3972858 = z;
        double r3972859 = log(r3972858);
        double r3972860 = r3972857 * r3972859;
        double r3972861 = t;
        double r3972862 = 1.0;
        double r3972863 = r3972861 - r3972862;
        double r3972864 = a;
        double r3972865 = log(r3972864);
        double r3972866 = r3972863 * r3972865;
        double r3972867 = r3972860 + r3972866;
        double r3972868 = b;
        double r3972869 = r3972867 - r3972868;
        double r3972870 = exp(r3972869);
        double r3972871 = r3972856 * r3972870;
        double r3972872 = r3972871 / r3972857;
        return r3972872;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3972873 = x;
        double r3972874 = exp(1.0);
        double r3972875 = a;
        double r3972876 = log(r3972875);
        double r3972877 = t;
        double r3972878 = 1.0;
        double r3972879 = r3972877 - r3972878;
        double r3972880 = r3972876 * r3972879;
        double r3972881 = z;
        double r3972882 = log(r3972881);
        double r3972883 = y;
        double r3972884 = r3972882 * r3972883;
        double r3972885 = r3972880 + r3972884;
        double r3972886 = b;
        double r3972887 = r3972885 - r3972886;
        double r3972888 = pow(r3972874, r3972887);
        double r3972889 = r3972873 * r3972888;
        double r3972890 = r3972889 / r3972883;
        double r3972891 = cbrt(r3972890);
        double r3972892 = cbrt(r3972891);
        double r3972893 = r3972892 * r3972892;
        double r3972894 = r3972892 * r3972893;
        double r3972895 = exp(r3972887);
        double r3972896 = r3972873 * r3972895;
        double r3972897 = r3972896 / r3972883;
        double r3972898 = cbrt(r3972897);
        double r3972899 = r3972898 * r3972898;
        double r3972900 = r3972894 * r3972899;
        return r3972900;
}

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 1.7

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

  3. Applied add-cube-cbrt1.7

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

  5. Applied *-un-lft-identity1.7

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

  6. Applied exp-prod1.7

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

  7. Simplified1.7

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

  9. Applied add-cube-cbrt1.7

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

  10. Final simplification1.7

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

Reproduce

herbie shell --seed 2019172 
(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))