Average Error: 1.9 → 0.9
Time: 55.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\log a \le -19.80479467655467:\\ \;\;\;\;\frac{\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log z \cdot y - b\right) + \left(t - 1.0\right) \cdot \log a}}}\\ \end{array}\]
\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}\;\log a \le -19.80479467655467:\\
\;\;\;\;\frac{\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r4724598 = x;
        double r4724599 = y;
        double r4724600 = z;
        double r4724601 = log(r4724600);
        double r4724602 = r4724599 * r4724601;
        double r4724603 = t;
        double r4724604 = 1.0;
        double r4724605 = r4724603 - r4724604;
        double r4724606 = a;
        double r4724607 = log(r4724606);
        double r4724608 = r4724605 * r4724607;
        double r4724609 = r4724602 + r4724608;
        double r4724610 = b;
        double r4724611 = r4724609 - r4724610;
        double r4724612 = exp(r4724611);
        double r4724613 = r4724598 * r4724612;
        double r4724614 = r4724613 / r4724599;
        return r4724614;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4724615 = a;
        double r4724616 = log(r4724615);
        double r4724617 = -19.80479467655467;
        bool r4724618 = r4724616 <= r4724617;
        double r4724619 = x;
        double r4724620 = t;
        double r4724621 = 1.0;
        double r4724622 = r4724620 - r4724621;
        double r4724623 = r4724622 * r4724616;
        double r4724624 = z;
        double r4724625 = log(r4724624);
        double r4724626 = y;
        double r4724627 = r4724625 * r4724626;
        double r4724628 = r4724623 + r4724627;
        double r4724629 = b;
        double r4724630 = r4724628 - r4724629;
        double r4724631 = exp(r4724630);
        double r4724632 = cbrt(r4724631);
        double r4724633 = r4724632 * r4724632;
        double r4724634 = r4724633 * r4724632;
        double r4724635 = r4724619 * r4724634;
        double r4724636 = cbrt(r4724626);
        double r4724637 = r4724636 * r4724636;
        double r4724638 = r4724635 / r4724637;
        double r4724639 = r4724638 / r4724636;
        double r4724640 = r4724627 - r4724629;
        double r4724641 = r4724640 + r4724623;
        double r4724642 = exp(r4724641);
        double r4724643 = r4724626 / r4724642;
        double r4724644 = r4724619 / r4724643;
        double r4724645 = r4724618 ? r4724639 : r4724644;
        return r4724645;
}

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 (log a) < -19.80479467655467

    1. Initial program 0.7

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

    3. Applied add-cube-cbrt0.7

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

    4. Applied associate-/r*0.7

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

    6. Applied add-cube-cbrt0.7

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

    if -19.80479467655467 < (log a)

    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

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

    5. Applied associate-/l*1.1

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

    6. Simplified1.1

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\left(\log z \cdot y - b\right) + \left(t - 1.0\right) \cdot \log a}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \le -19.80479467655467:\\ \;\;\;\;\frac{\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{e^{\left(\left(t - 1.0\right) \cdot \log a + \log z \cdot y\right) - b}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log z \cdot y - b\right) + \left(t - 1.0\right) \cdot \log a}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 
(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))