Average Error: 2.1 → 2.1
Time: 14.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -2.9642058948872463 \cdot 10^{33} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -335.233961090993546\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;\left(t - 1\right) \cdot \log a \le -2.9642058948872463 \cdot 10^{33} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -335.233961090993546\right):\\
\;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r29830 = x;
        double r29831 = y;
        double r29832 = z;
        double r29833 = log(r29832);
        double r29834 = r29831 * r29833;
        double r29835 = t;
        double r29836 = 1.0;
        double r29837 = r29835 - r29836;
        double r29838 = a;
        double r29839 = log(r29838);
        double r29840 = r29837 * r29839;
        double r29841 = r29834 + r29840;
        double r29842 = b;
        double r29843 = r29841 - r29842;
        double r29844 = exp(r29843);
        double r29845 = r29830 * r29844;
        double r29846 = r29845 / r29831;
        return r29846;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r29847 = t;
        double r29848 = 1.0;
        double r29849 = r29847 - r29848;
        double r29850 = a;
        double r29851 = log(r29850);
        double r29852 = r29849 * r29851;
        double r29853 = -2.9642058948872463e+33;
        bool r29854 = r29852 <= r29853;
        double r29855 = -335.23396109099355;
        bool r29856 = r29852 <= r29855;
        double r29857 = !r29856;
        bool r29858 = r29854 || r29857;
        double r29859 = x;
        double r29860 = y;
        double r29861 = z;
        double r29862 = log(r29861);
        double r29863 = r29860 * r29862;
        double r29864 = r29863 + r29852;
        double r29865 = b;
        double r29866 = r29864 - r29865;
        double r29867 = exp(r29866);
        double r29868 = r29859 * r29867;
        double r29869 = r29868 / r29860;
        double r29870 = pow(r29861, r29860);
        double r29871 = pow(r29850, r29849);
        double r29872 = exp(r29865);
        double r29873 = r29871 / r29872;
        double r29874 = r29870 * r29873;
        double r29875 = r29860 / r29874;
        double r29876 = r29859 / r29875;
        double r29877 = r29858 ? r29869 : r29876;
        return r29877;
}

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 (* (- t 1.0) (log a)) < -2.9642058948872463e+33 or -335.23396109099355 < (* (- t 1.0) (log a))

    1. Initial program 1.1

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

    if -2.9642058948872463e+33 < (* (- t 1.0) (log a)) < -335.23396109099355

    1. Initial program 6.6

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

    3. Applied associate-/l*2.1

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

    4. Simplified6.8

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -2.9642058948872463 \cdot 10^{33} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -335.233961090993546\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))