Average Error: 2.0 → 1.5
Time: 53.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.874142655497601 \cdot 10^{-203}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}}\right)\\ \mathbf{elif}\;x \le 4.564051854504764 \cdot 10^{+138}:\\ \;\;\;\;\frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)} \cdot x}{y}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.874142655497601 \cdot 10^{-203}:\\
\;\;\;\;\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}}\right)\\

\mathbf{elif}\;x \le 4.564051854504764 \cdot 10^{+138}:\\
\;\;\;\;\frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{{e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)} \cdot x}{y}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r3639746 = x;
        double r3639747 = y;
        double r3639748 = z;
        double r3639749 = log(r3639748);
        double r3639750 = r3639747 * r3639749;
        double r3639751 = t;
        double r3639752 = 1.0;
        double r3639753 = r3639751 - r3639752;
        double r3639754 = a;
        double r3639755 = log(r3639754);
        double r3639756 = r3639753 * r3639755;
        double r3639757 = r3639750 + r3639756;
        double r3639758 = b;
        double r3639759 = r3639757 - r3639758;
        double r3639760 = exp(r3639759);
        double r3639761 = r3639746 * r3639760;
        double r3639762 = r3639761 / r3639747;
        return r3639762;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3639763 = x;
        double r3639764 = -1.874142655497601e-203;
        bool r3639765 = r3639763 <= r3639764;
        double r3639766 = a;
        double r3639767 = log(r3639766);
        double r3639768 = t;
        double r3639769 = 1.0;
        double r3639770 = r3639768 - r3639769;
        double r3639771 = r3639767 * r3639770;
        double r3639772 = y;
        double r3639773 = z;
        double r3639774 = log(r3639773);
        double r3639775 = r3639772 * r3639774;
        double r3639776 = r3639771 + r3639775;
        double r3639777 = b;
        double r3639778 = r3639776 - r3639777;
        double r3639779 = exp(r3639778);
        double r3639780 = sqrt(r3639779);
        double r3639781 = r3639780 * r3639780;
        double r3639782 = r3639763 * r3639781;
        double r3639783 = r3639782 / r3639772;
        double r3639784 = cbrt(r3639783);
        double r3639785 = r3639784 * r3639784;
        double r3639786 = r3639784 * r3639785;
        double r3639787 = 4.564051854504764e+138;
        bool r3639788 = r3639763 <= r3639787;
        double r3639789 = cbrt(r3639772);
        double r3639790 = r3639779 / r3639789;
        double r3639791 = r3639789 * r3639789;
        double r3639792 = r3639763 / r3639791;
        double r3639793 = r3639790 * r3639792;
        double r3639794 = exp(1.0);
        double r3639795 = pow(r3639794, r3639778);
        double r3639796 = r3639795 * r3639763;
        double r3639797 = r3639796 / r3639772;
        double r3639798 = r3639788 ? r3639793 : r3639797;
        double r3639799 = r3639765 ? r3639786 : r3639798;
        return r3639799;
}

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 3 regimes

  2. if x < -1.874142655497601e-203

    1. Initial program 1.6

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

    3. Applied add-sqr-sqrt1.6

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

    5. Applied add-cube-cbrt1.6

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

    if -1.874142655497601e-203 < x < 4.564051854504764e+138

    1. Initial program 2.8

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

    3. Applied add-cube-cbrt2.8

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

    4. Applied times-frac1.6

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

    if 4.564051854504764e+138 < x

    1. Initial program 0.6

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

    3. Applied *-un-lft-identity0.6

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

    4. Applied exp-prod0.6

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

    5. Simplified0.6

      \[\leadsto \frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.874142655497601 \cdot 10^{-203}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}{y}}\right)\\ \mathbf{elif}\;x \le 4.564051854504764 \cdot 10^{+138}:\\ \;\;\;\;\frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)} \cdot x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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))