Average Error: 2.0 → 2.4
Time: 34.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -0.01453486137960070465058315392070653615519 \lor \neg \left(b \le -1.935658811926314331032579532956646040497 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;b \le -0.01453486137960070465058315392070653615519 \lor \neg \left(b \le -1.935658811926314331032579532956646040497 \cdot 10^{-77}\right):\\
\;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r62820 = x;
        double r62821 = y;
        double r62822 = z;
        double r62823 = log(r62822);
        double r62824 = r62821 * r62823;
        double r62825 = t;
        double r62826 = 1.0;
        double r62827 = r62825 - r62826;
        double r62828 = a;
        double r62829 = log(r62828);
        double r62830 = r62827 * r62829;
        double r62831 = r62824 + r62830;
        double r62832 = b;
        double r62833 = r62831 - r62832;
        double r62834 = exp(r62833);
        double r62835 = r62820 * r62834;
        double r62836 = r62835 / r62821;
        return r62836;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r62837 = b;
        double r62838 = -0.014534861379600705;
        bool r62839 = r62837 <= r62838;
        double r62840 = -1.9356588119263143e-77;
        bool r62841 = r62837 <= r62840;
        double r62842 = !r62841;
        bool r62843 = r62839 || r62842;
        double r62844 = x;
        double r62845 = y;
        double r62846 = z;
        double r62847 = log(r62846);
        double r62848 = r62845 * r62847;
        double r62849 = t;
        double r62850 = 1.0;
        double r62851 = r62849 - r62850;
        double r62852 = a;
        double r62853 = log(r62852);
        double r62854 = r62851 * r62853;
        double r62855 = r62848 + r62854;
        double r62856 = r62855 - r62837;
        double r62857 = exp(r62856);
        double r62858 = r62844 * r62857;
        double r62859 = r62858 / r62845;
        double r62860 = pow(r62846, r62845);
        double r62861 = pow(r62852, r62851);
        double r62862 = exp(r62837);
        double r62863 = r62861 / r62862;
        double r62864 = r62860 * r62863;
        double r62865 = r62864 / r62845;
        double r62866 = r62844 * r62865;
        double r62867 = r62843 ? r62859 : r62866;
        return r62867;
}

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 b < -0.014534861379600705 or -1.9356588119263143e-77 < b

    1. Initial program 1.8

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

    if -0.014534861379600705 < b < -1.9356588119263143e-77

    1. Initial program 4.6

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

    3. Applied *-un-lft-identity4.6

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

    4. Applied times-frac3.3

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

    5. Simplified3.3

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

    6. Simplified11.1

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -0.01453486137960070465058315392070653615519 \lor \neg \left(b \le -1.935658811926314331032579532956646040497 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))