Average Error: 2.1 → 2.1
Time: 14.6s
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 r48660 = x;
        double r48661 = y;
        double r48662 = z;
        double r48663 = log(r48662);
        double r48664 = r48661 * r48663;
        double r48665 = t;
        double r48666 = 1.0;
        double r48667 = r48665 - r48666;
        double r48668 = a;
        double r48669 = log(r48668);
        double r48670 = r48667 * r48669;
        double r48671 = r48664 + r48670;
        double r48672 = b;
        double r48673 = r48671 - r48672;
        double r48674 = exp(r48673);
        double r48675 = r48660 * r48674;
        double r48676 = r48675 / r48661;
        return r48676;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r48677 = t;
        double r48678 = 1.0;
        double r48679 = r48677 - r48678;
        double r48680 = a;
        double r48681 = log(r48680);
        double r48682 = r48679 * r48681;
        double r48683 = -2.9642058948872463e+33;
        bool r48684 = r48682 <= r48683;
        double r48685 = -335.23396109099355;
        bool r48686 = r48682 <= r48685;
        double r48687 = !r48686;
        bool r48688 = r48684 || r48687;
        double r48689 = x;
        double r48690 = y;
        double r48691 = z;
        double r48692 = log(r48691);
        double r48693 = r48690 * r48692;
        double r48694 = r48693 + r48682;
        double r48695 = b;
        double r48696 = r48694 - r48695;
        double r48697 = exp(r48696);
        double r48698 = r48689 * r48697;
        double r48699 = r48698 / r48690;
        double r48700 = pow(r48691, r48690);
        double r48701 = pow(r48680, r48679);
        double r48702 = exp(r48695);
        double r48703 = r48701 / r48702;
        double r48704 = r48700 * r48703;
        double r48705 = r48690 / r48704;
        double r48706 = r48689 / r48705;
        double r48707 = r48688 ? r48699 : r48706;
        return r48707;
}

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))