Average Error: 2.0 → 2.0
Time: 2.8m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \left(\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \left(\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r27102819 = x;
        double r27102820 = y;
        double r27102821 = z;
        double r27102822 = log(r27102821);
        double r27102823 = r27102820 * r27102822;
        double r27102824 = t;
        double r27102825 = 1.0;
        double r27102826 = r27102824 - r27102825;
        double r27102827 = a;
        double r27102828 = log(r27102827);
        double r27102829 = r27102826 * r27102828;
        double r27102830 = r27102823 + r27102829;
        double r27102831 = b;
        double r27102832 = r27102830 - r27102831;
        double r27102833 = exp(r27102832);
        double r27102834 = r27102819 * r27102833;
        double r27102835 = r27102834 / r27102820;
        return r27102835;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r27102836 = x;
        double r27102837 = a;
        double r27102838 = log(r27102837);
        double r27102839 = t;
        double r27102840 = 1.0;
        double r27102841 = r27102839 - r27102840;
        double r27102842 = r27102838 * r27102841;
        double r27102843 = z;
        double r27102844 = log(r27102843);
        double r27102845 = y;
        double r27102846 = r27102844 * r27102845;
        double r27102847 = r27102842 + r27102846;
        double r27102848 = b;
        double r27102849 = r27102847 - r27102848;
        double r27102850 = exp(r27102849);
        double r27102851 = r27102836 * r27102850;
        double r27102852 = 1.0;
        double r27102853 = r27102852 / r27102845;
        double r27102854 = r27102851 * r27102853;
        double r27102855 = cbrt(r27102854);
        double r27102856 = r27102855 * r27102855;
        double r27102857 = r27102855 * r27102856;
        return r27102857;
}

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 2.0

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}}\]
  4. Using strategy rm

  5. Applied div-inv1.9

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\color{blue}{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}}\]
  6. Using strategy rm

  7. Applied div-inv2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\color{blue}{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}}\right) \cdot \sqrt[3]{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}\]
  8. Using strategy rm

  9. Applied div-inv2.0

    \[\leadsto \left(\sqrt[3]{\color{blue}{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}} \cdot \sqrt[3]{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}\right) \cdot \sqrt[3]{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}\]

  10. Final simplification2.0

    \[\leadsto \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \left(\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}}\right)\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(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))