Average Error: 1.8 → 1.8
Time: 50.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left(\sqrt[3]{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\right)\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left(\sqrt[3]{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\right)\right)}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r3156712 = x;
        double r3156713 = y;
        double r3156714 = z;
        double r3156715 = log(r3156714);
        double r3156716 = r3156713 * r3156715;
        double r3156717 = t;
        double r3156718 = 1.0;
        double r3156719 = r3156717 - r3156718;
        double r3156720 = a;
        double r3156721 = log(r3156720);
        double r3156722 = r3156719 * r3156721;
        double r3156723 = r3156716 + r3156722;
        double r3156724 = b;
        double r3156725 = r3156723 - r3156724;
        double r3156726 = exp(r3156725);
        double r3156727 = r3156712 * r3156726;
        double r3156728 = r3156727 / r3156713;
        return r3156728;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3156729 = x;
        double r3156730 = a;
        double r3156731 = log(r3156730);
        double r3156732 = t;
        double r3156733 = 1.0;
        double r3156734 = r3156732 - r3156733;
        double r3156735 = r3156731 * r3156734;
        double r3156736 = z;
        double r3156737 = log(r3156736);
        double r3156738 = y;
        double r3156739 = r3156737 * r3156738;
        double r3156740 = r3156735 + r3156739;
        double r3156741 = b;
        double r3156742 = r3156740 - r3156741;
        double r3156743 = exp(r3156742);
        double r3156744 = cbrt(r3156743);
        double r3156745 = r3156744 * r3156744;
        double r3156746 = r3156744 * r3156745;
        double r3156747 = cbrt(r3156746);
        double r3156748 = sqrt(r3156743);
        double r3156749 = r3156748 * r3156748;
        double r3156750 = cbrt(r3156749);
        double r3156751 = r3156745 * r3156750;
        double r3156752 = cbrt(r3156751);
        double r3156753 = r3156744 * r3156752;
        double r3156754 = r3156747 * r3156753;
        double r3156755 = r3156729 * r3156754;
        double r3156756 = r3156755 / r3156738;
        return r3156756;
}

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 1.8

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

  3. Applied add-cube-cbrt1.8

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

  5. Applied add-cube-cbrt1.8

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

  7. Applied add-cube-cbrt1.8

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

  9. Applied add-sqr-sqrt1.8

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

  10. Final simplification1.8

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

Reproduce

herbie shell --seed 2019139 
(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))